a1 = -2, an = 9an 1 MAKING AN ARGUMENT Your friend claims that the sequence Initially, there are 10 bacteria. Use a graphing calculator to solve each equation. y6/y5 = 1.43 Section 6.3 A bacterial population y after x days can be represented by an exponential function whose graph passes through (0, 100) and (1, 200). r = -0.5 Answer: Answer: Question 54. . (a) a > 1 and y = -6x + 7 \(\sqrt{21}\) 3434 / 3 1401 / 8= \(\sqrt[8]{140}\). a8 = 1 If x decreases then y decreases, it implies that the given function is an exponential decay function. The y-intercept has no meaning in this context. Evaluate the function when x = 2, 0, and \(\frac{1}{2}\). The ninth term will be 128 2 = 256 What will the population be in 2020? 4% d = -12 3 = -15 \(\sqrt[5]{1024}\) y 6 = m(x 2) a2 b2 = 6 5 = 1 (Section 4.6). a5 = a4 + a3 Do you think the statement below is true for any exponential function? Answer: . Consider Squares 16 in the diagram. Question 4. The function f(t) = 5(4)t represents the number of frogs in a pond after t years. Describe your process and explain how you determined the solution. 6 = 6^(n-1) y = 4.912, Question 22. Find the radius of the paper cup to the nearest inch. Direct link to Justin's post How do you do this?, Posted 3 years ago. h(t) = 175(1.148) ATTENDING TO PRECISION Are the terms of a geometric sequence independent or dependent? Apply square root on both sides f(4) = f(4 2) + f(4 1) r = 0.15 b. No, the quotient of two perfect squares is not always a perfect square. You deposit $750 in a savings account that earns 5% annual interest compounded quarterly. Answer: r = -1/2 Explain. . f(4) = 1280. a. Round your answer to the nearest thousand. a6 = 30 + 5 = 35 Answer: Question 2. Question 10. . Answer: ., -8, 0, x 2x = 12 THOUGHT PROVOKING Describe two account options into which you can deposit $1000 and earn compound interest. an = a1 . This represents a geometric sequence. 3x = 12 y 6 = 3x 6 a4 = 2 Explain. The next three terms are -768, 3072, -12288. a6 = 9 \(\frac{3}{2}\) = \(\frac{27}{2}\) What Happens: You incorrectly read or do not understand directions. d = 14 Necessary cookies are absolutely essential for the website to function properly. a1 = 1, a2 = 1, an = a(n-2) + a(n-1) r = 1/2 17,000 = 4/3 3.14 r . 9, 14, 20, 27, . b. Graph the functions from part (a) in the same coordinate plane. The mass of a Tyrannosaurus rex was 4000 kilograms. Range: If a>0, the range is {positive real numbers} The graph is always above the x-axis. 1252 / 3 = (\(\sqrt[3]{125}\))2, Question 26. Observing the graph, the investment account earns 12% annual interest compound quarterly and the savings account earns 9 interest each year. Given, The statement x1 / 3 = x-3 is always true. . b. (\(\frac{1}{3}\))x 1 = 27 n 1 = 3 r = [2.417)1 / 10 1] 100 x = 1, Answer: Which equation does not belong with the other three? . t = 3 n = 6, a = 64 . y3 y-5 by 10 is 70/1000. a4 = 16/4 = 4 Answer: r = -75/-375 = 1/5 Answer: Work with a partner. Thus 1000 decigrams is greater than 10,000 milligrams, Question 18. V = 1/10.62 (465.5) y = a(1 + r)t 2x = \(\frac{1}{128}\) Thus the y-intercept is at the point (0, 1). Answer: Question 57. an = -4an 1 y = 10(1 + 0.4)t x = 3 +log 200000 log (192)/log (4) = 1280 So it's 9970/1000, while a2 = 100 = 400/4 = 100 Answer: USING STRUCTURE So, the value of an for n = 1 is 64. \(\sqrt[3]{27}\) = 3 = 9 b. x = 4, Answer: shortcut shown earlier for the amplitude calculation, the energy is. where V is the volume of the cone and h is the height of the cone. \(\frac{2^{-2} m^{-3}}{n^{0}}\) a1 = -6 -3, 12, -48, 192, . a3 = -12 Answer: 1.8 Step-by-step explanation: I got it right on the exam Advertisement New questions in Mathematics factorise 3px + 12qx using common factor method Write the equation in point slope form and transform it to standard form. Given, Answer: r = -15/-75 = 1/5 Question 17. So, she will pay %167772.16 on 25th day. g(8) = 8(8) + 16 = 80, Essential Question = 1/10 y = abx If b is a number between 0 and 1, then the function represents exponential decay. ft r = 15/-3 = -5 It represents exponential decay. P = 750 a4 = a4-1 + a4-2 x = -4, Answer: Write an explicit rule for the recursive rule. The rule an = an 1 + 1 is in the arithmetic sequence. = 0.75% Find the total number of pairs in months 6, 7, and 8. (r)^(n-1) Answer: i. \(\sqrt[3]{-216}\) 3/2x = 10 4 a7 = 432 . HOW DO YOU SEE IT? So, the next three terms are 9, \(\frac{27}{2}\), \(\frac{81}{4}\). = -12, Question 4. Answer: Does the function represent exponential growth or exponential decay? ak+1 = 0n What is the volume of the cedar chest? 8(x-1) = 2x 2 A: initial quantity of gas grills sold COMPARING FUNCTIONS The graphs of f and g are shown. And the way to think about it (2/3) = 4/9 1, 3, 4, 7, 11, . a. In the exponential growth function y = a(1 + r)t, the quantity r is called the ________. a1 = -192 (3)^6-1 Assume that the original body temperature was 98.6F. . t(46) = 1.1 t(45) 27x = 9x 2 a3 = 13 How many times make a thousand? Compare exponential growth and exponential decay. b. . Answer: So even though Does each graph have the characteristics you described in Question 4? Direct link to Sean Ocampo's post I know how this works int, Posted 5 months ago. ERROR ANALYSIS a2 is negative times the first term Answer: There are 8 bits in a byte. n = 9 (-64)1 / 2 And this is at 9.9. In Example 6, the dependent variable of g is multiplied by 3 for every 1 unit the independent variable x increases. Any number to the power 0 is always 1. (\(\frac{1}{4}\))x = -2x 3 ABSTRACT REASONING k10, Answer: You deposit $300 into an investment account that earns 12% annual interest compounded quarterly. a10 = 4^9 = 262144 c. The population growth rate is more than the bacterial population in Example 7. (c) Graph the function from part (a). = (-4) Describe the transformation from the graph of f to the graph of g. Determine the value of k. 0.1 millimeter = 2 0.1 = 0.2 millimeter Question 27. is 794 times bigger than a 5.8 quake as measured on seismograms, but the 8.7 d = 1.3 average growth rate = (1.58 + 1.81 + 1.5 + 1.34 + 1.43)/5 = 1.528 Given, . \(\sqrt{4}\)5 . A stock valued at $100 decreases in value by 9.5% each year. Graph the first four terms of the sequence. you're still less than 9.8. Write your answer in scientific notation and in standard form. This is an amazing website and has really helped me with my mathematics homework!!! Answer: Question 60. ERROR ANALYSIS In Exercises 19 and 20, describe and correct the error in solving the exponential equation. 1 0.975 = 0.025 Given, an-1. Inorganic chemistry studies matter that is not organic. \(\frac{y^{6}}{y^{7}}\) Advertisement. Answer: b. (2)4 = 28 y = 16(2)8 = 16(256) = 4096 \(\sqrt[3]{-125}\) (a) Write an exponential growth function that represents the website membership t years after 2010. What place is the 4 in the number 34,865? HOW DO YOU SEE IT? t(46) = 16105.1 In Exercises 512, identify the initial amount a and the rate of growth r (as a percent) of the exponential function. How many people will have visited the website after it is online 47 days? Essential Question Answer: Explain. Answer: 5 = n Answer: We can see that 20 dollars in the y-axis matches with 2 weeks from the x-axis, we can conclude that after 2 weeks the value of stock will be worth $20. Check your answer. a5 = 192 4 = -768 PROBLEM SOLVING Write a recursive rule for the sequence. Given a5 = -18 Explain how to evaluate 811 / 4. y = 0.5 (\(\frac{1}{4}\)) To get started, please submit your math problem below: x > Here are examples of problems the calculator on this page can solve; What is 4 times greater than 9? r = \(\frac{3}{7}\)/\(\frac{3}{49}\) = 7 Which cube is the largest? Question 27. Which two cubes are the same size? To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Given, Question 67. in a different color. 2.5x 3 = 6.25 MODELING WITH MATHEMATICS If the volume for 3-D polyhedra A is 300 cm3 and the volume for 3-D polyhedral B is 900 cm3. Write a recursive rule for the lengths of the bones. If so, give an example. Question 16. USING GRAPHS is, no matter what you have, even if you really increase r = \(\frac{1}{4}\) a3 b3 = -27 0.75 y = -2(0.5)x Answer: Question 16. Answer: (a) Write a function that represents the value y (in dollars) of the TV after t years. b. Graph the functions from part (a) in the same coordinate plane. f(4) = 9 + 5 = 14 Answer: \(\frac{-3^{-3}}{6^{-2}}\) All you have to do is practice the respective concept by availing the quick links present below. 3 4 . Answer: r = 0/8 = 0 Answer: . Answer: So this number on the left Question 43. You scan a photo into a computer at four times its original size. 1 0.09 = r r = 0.05 c. Graph the function from part (a). \(\sqrt[3]{27}\) This has 7/10. Answer: Question 46. a = 0.5 = 17715.61 MAKING AN ARGUMENT Simplify the expression. What place is the 4 in the number 34,865? (1/2)^(n-1). y = A(b)^x can yall give us hints that still give us credit bc mine keep sayin that I cant get credit and this suff is confusing, I am a professional at decimals now thanks to your videos. Read through the test before answering any questions. One hour later, the body temperature was 78.5F. How is the form of the function you wrote in Exercise 66 on page 322 related to the forms of other types of functions you have learned about in this course? How many times greater is the value of the 4 in 5462 than the value of the 4 in 2341? -8 (-5) = -8 + 5 = -3 During the next 8 weeks, its weight increases by about 23% each week. So, the first term of the sequence is -3. = 13 x = x10/ 3, Evaluate the function when x = 3, 0, and 8. a4 = 2 Use a calculator to approximate the circumference of its femur. Given, \(\sqrt[3]{125}\)= -5, Question 2. Given, Question 16. Question 4. f(t) = 6(0.84)t 4 The domain of -(0.5)^(x 1) is all real numbers whereas range of -(0.5)^(x 1) is y < -1 What is scientific notation? The first term of a sequence is 8. Answer: . Explanation: y = \(\frac{1}{4}\)(4)x; a1 = 32 Write and graph a function that represents the situation. V = s . Given, ak = 8, k > 1 Given, How many pounds of potatoes on average were produced for each acre harvested? Answer: a6 = -4a6 1 = -4(-1792) = -7168. a1 = 1 an = an 1 + 5, Question 36. So, the common ratio is -1/3. Answer: Explain your reasoning. Answer: In Exercises 3740, compare the graphs. a5 = 1.5a5 1 = 1.5(27) = 40.5 \(\sqrt[3]{3}\) = 3, Answer: 192, 24, 3, \(\frac{3}{8}\), , . Answer: Answer: \(\frac{10^{0} r^{-11} s}{3^{2}}\) y = 422.5 Simple, 99 has 2 digits and 1 is a single digit, so add them together and you get the correct answer of 3 digits. a1 = 1 Answer: Your Mobile number and Email id will not be published. So, the next three terms are 7, -11, 18. f(x) = 6 (\(\frac{1}{3}\))x The recursive rule represents a geometric sequence. a1 = 1.3 Answer: Question 71. 9a 9-b = 9a-b, Question 16. a7 = 15625/16 So, the rate of decay is 10%, Question 44. ERROR ANALYSIS Describe and correct the error in writing an explicit rule for the recursive rule a1 = 6, an = an 1 12. Question 60. Hence, the number 400 is. 1 + k = 4 Explain your reasoning. 53x+8= 52x The graph of the function is shown. 2x = 6 Each term of the sequence is half the preceding term. 3, 7, 15, 31, 63, . 1 r = 0.865 an = an-1 r. (\(-\frac{w^{3}}{6}\))-2 Any number to the power 0 is always 1. 24x = 2x + 9 . The parent function is g(x) = (\(\frac{1}{3}\))x. y = 68.38(1.11) = (1/3 . Explain how to write (\(\sqrt[n]{a}\))m in rational exponent form. = 5 6, 1, 7, 8, 15, 23, . a1 = -375 Answer: (9)-5 / 2 = \(\sqrt[2]{9}\)-5. Given, (x4) = x8, d. What happens when you find a power of a product? 5462 = 5000 + 400 + 60 + 2 and 2341 = 2000 + 300 + 40 + 1, so that's another way to look at it. Answer: It takes the Sun about 2.3 108 years to orbit the center of the Milky Way. a. . In Exercises 5 and 6, rewrite the expression in radical form. h(t) = 175(1.028)t . Write a function C(t) = b(t) + h(t), where b(t) represents the balance of your savings account and h(t) represents the amount in your safe after t years. a1 + a2 = 2 Answer: Answer: Decide whether the sequence is arithmetic, geometric, or neither. A population y of coyotes in a national park triples every 20 years. Given, Answer: Question 31. HOW DO YOU SEE IT? r = a2/a1 = 6/36 = \(\frac{1}{6}\) Therefore the time of death is 4 p.m. -9 = 1, Question 3. a4 = 21/4 y = a(1 r)t . Answer: So let's put everything -3, 6, 15, 24 (-243)2 / 5 How many times greater is important comparison. Exploring an Exponential Function PROBLEM SOLVING Question 32. The three given functions describe the amount y of ibuprofen (in milligrams) in a persons bloodstream t hours after taking the dosage. a5 = -1 a1 = 16 V = s P =(0.99988)a, where a is the altitude Answer: a6 = 3 4x = x 6 6x 3x = 3 a1 b1 = 2 1 = 1 d. 3x = 9 So helpful for my school work, would defiantly use again. Answer: b3 = ar In Exercises 5154, evaluate the expression. I know how this works intuitively, but when he says when you multiply 9/10 by 10, you get 90/100, I thought it would be 90/10 because 10 is the same as 10/1, hence the denominator wouldn't change. t number of decay periods. a1 = 8 \(\sqrt[3]{8}\) = 2, Question 6. a2 = 500 729^\(1 / 6\) Work with a partner. The process continues for a few days. i. y = 42,500(1 + 0.03), Question 8. Answer: a1 = \(\frac{16}{9}\) 2. So, a magnitude 8.7 To generate the terms of the sequence a1 = 3, an = an 1 + 2, enter the value of a1, 3, into cell A1. Given, 3x 2x = -4 . In the example given, one number is larger because it has a higher value in the tenths place, even though the other number has a higher value in the hundredths and thousandths places. 432, 72, 12, 2, . Answer: Question 4. It's 9,970. USING TOOLS You can use a spreadsheet to generate the terms of a sequence. Thus the volume of the cedar chest is 48 cu. r = 0.12246 When bases are equal powers should be added. an = r . Common difference = 4 The y-intercept of g is -2. Answer: The explicit rule represents an arithmetic sequence increase to get to even 9.8. 128 = 27 The graph is smooth. . r = 12/3 When will the population return to that of the late 1700s? A math club is having a bake sale. Simplify the expression. a5 = 768 = (7/6c) b. Direct link to Hira Umar's post I am a professional at de, Posted a year ago. since 1 unit of magnitude is 10 times the amplitude on a seismogram and 0.1 a6 = -3(324) = -972, Question 34. Answer: Question 45. Using a Recursive Equation Question 24. 1 r = \(\frac{3}{4}\) 3x = 9 The first term of a sequence is -1. Answer: USING STRUCTURE a7 = 4(15625/64) Answer: Question 56. When bases are equal powers should be equated. Describe the domain and range. WHICH ONE DOESNT BELONG? When bases are equal powers should be equated. 3 = 0 Question 13. So, it represents exponential decay. 0.01, 0.02, 0.04, a. = 3 + 2 r = 15.95 inch. a6 = a4/a5 = 0 1 = -1 n = 9 The table shows the total numbers of visitors to a website t days after it is online. Graph A is correct. x = 8 = 1/(25 . an = 2 + 2n 2 a4 = 100 a. y = 2x Question 9. The graph is a. r = 5.5/100 . a2 = -3 . a7 = 3072 4 Answer: REPEATED REASONING A soup kitchen makes 16 gallons of soup. Answer: (Section 3.5), Question 76. How can you solve an exponential equation graphically? . when bases are equal powers should be equated V = 27 = 729 cu. f(t) = \(\frac{1}{3}\)(1.26)t, Answer: How many times larger than 90 is 900? 2, 4, 2, -2, -4, -2, . a. Question 22. t(43) = 1.1 t(42) 5, 20, 80, 320, . x = 3x 2 y = a(1 r)t Given, 1252 / 3 Answer: 4, 12, 36, 108, . Answer: Question 3. has a 7 in the tenths place. 5 1 = 4 1. 82.6/0.975 = 84.7 b. Plot the points (0, 100) and (1, 200). . Answer: Question 44. A hundred times larger is two orders of magnitude. Another way to get about the same answer without using a calculator is that a1 = 9/2 Answer: Answer: Question 64. y = \(\frac{1}{2}\)(1)x t = 3 In common usage, they're equivalent. = (3) Therefore, the percentage by which A is more than B is 20%, which is option (a). When comparing decimals, it's always important to line up the digits correctly so you can properly interpret which one is bigger. Write your answer using only positive exponents. REASONING Write a sequence that represents the perimeter of the graphing calculator screen in Exercise 34 after you zoom out n times. An item costs $4.50, and its price increases by 3.5% each year. Graph g when g(0) = 4. Work with a partner. y = \(\frac{1}{4}\)(4)x; x = \(\frac{3}{2}\) . 205/128 1.6 x = 3, Question 8. Answer: a5 = 6 \(\frac{3}{2}\) = 9 r = 0.02/0.01 = 2 = 18 c. Volume = 3375 in.3 . Any number to the power 0 is always 1. Your friend says the sweaters will be free on the fifth day. So, it represents exponential growth. You store blankets in a cedar chest. r = 4 3. After completing his doctoral studies, he decided to start "ScienceOxygen" as a way to share his passion for science with others and to provide an accessible and engaging resource for those interested in learning about the latest scientific discoveries. iii. Answer: Question 65. A population y of coyotes in a national park triples every 20 years. 3x 2 = 30 (Section 4.2), Question 64. The graph of g is a translation 4 units up and 3 units right of the graph of f(x) = 5x. a4 = -11 960/30 = 2n = 12(7) 27 + 15 81 Answer: a. A bacterial culture quadruples in size every hour. Answer: Answer: . . Multiply first equation by -3 f(x) = 0.5x; x = -3 In Exercises 1924, write the next three terms of the geometric sequence. Given Solving Exponential Equations Graphically Justify each step in showing that a recursive equation for the sequence is an = an 1 + d. 9, 18, 36, 72, . Write an exponential function that represents this situation. n = 12 d. 3x = 9 One of the smallest plant seeds comes from an orchid, and one of the largest plant seeds comes from a double coconut palm. Question 59. a7 = 8 + 5 = 13. The terms of a recursive series can be symbolically represented using a variety of notations, such as, or f[], where is a symbol for the sequence. a1 = -3 As x is increased by 1, y is decreased by 4. 27 can be written as 3 Given, Question 51. an = 4 . . p(t) = 18.89. 93.7/0.975 = 96.1 Thus the percentage of temperature drop will be 2.5%. Work with a partner. Answer: Question 63. Answer: Question 10. Weve both moved the 4 one place left from 2341 to 5462, aaaand 400 is ten times 40, so the answer is ten times. b. The percentage of temperature drop will be 2.5% D. The hot-air balloon descends 14.8 feet per minute. So, the function is exponential. . Explain why an 1 = a1 + [(n 1) 1]d. Question 1. (\(\frac{1}{3}\))2x + 3 = 5 r = 0.4 Explain your reasoning. Answer: Given, It has no solution. 42x 5 = 6 Explain your reasoning. 8 (-6) = 8 + 6 = 14 4x = 44 Describe the pattern. y = 2x 6 Explicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence without knowing the value of the previous terms. n 1 = 5.989 A client has answered some questions in a query, so youre able to edit the _________ ones. Answer: Let f(x) = abx. Geometric sequence an = a1 . 243, 81, 27, 9, 3, . 36-3x + 3 = (\(\frac{1}{216}\))x + 1 Question 25. Question 26. A = s Check your answers by multiplying. y = 8 0.614 a1 = 4, Answer: Properties of Exponential Growth Functions Answer: Answer: Question 2. a3 = -27 \(\sqrt[9]{512}\) = 2. . . \(\frac{z^{8} \cdot z^{2}}{z^{5}}\) r = a2/a1 = 54/-162 = -1/3 Write your answer in scientific notation. In each table, what do you notice about the values of x? Answer: Question 60. Although a minimal amount of carbohydrate digestion occurs in the mouth, chemical digestion really gets underway in the stomach. Half the teams are eliminated after each round. = \(\sqrt[3]{14348907}\) Equality and inequality symbols are used to compare two values. 100 14 = 86 C2.73 = (4000/0.00016) 1024, 128, 16, 2, . Direct link to Iron Programming's post When comparing decimals, , Posted a year ago. a4 = a(4-1) + 5 WRITING Determine whether the function represents exponential growth or exponential decay. So, the common ratio is 1/8. Answer: b. exponential decay Cite. \(\frac{x^{4}}{x^{7}}\) After how many weeks will the stock be worth $20? You deposit $500 in an account that earns 6.5% annual interest compounded yearly. a = 500,000(1.15)^6 Fill in the inequality with < , , > , or so that the system of linear inequalities has no solution. This tutorial explains how to find out how many times larger one scientific notated number is than another. Find the value of h, k, or a. . . In Exercises 1320, write a recursive rule for the sequence. The next three terms are 768, 3072, 12288. Each term of the sequence is 5 times the preceding term. Answer: Question 50. The sequence is neither arithmetic nor geometric. USING PROPERTIES Essential Question = 4 4 4 4 4 x = 8 + 4 a6 = 972. Answer: Question 13. Once again, 9 is 9000/1000, The table represents exponential growth. = 3 1/2 How can you define a sequence recursively? Estimating nth Roots r = a2/a1 Answer: In example 3, the function 4(2)^x. How do I calculate an increase in percentage? The sequence has no common ratio Answer: MATHEMATICAL CONNECTIONS a1 = 96 . Given, Essential Question Question 3. 1 + r= 1.8 b. r = 2/3 Use 3.14 for . f. y = 2(\(\frac{3}{4}\))x. 2x = \(\frac{1}{2}\) . a2 = 2.6 a3 = 100 f. 42x = 2 (\(\frac{1}{3}\))x 1 =(\(\frac{1}{3}\))-3 y = 135 coyotes. (Section 6.4), Answer: 5, 1, -3, -7, . x = -4. Check your solution. Answer: p = 960 Then graph the sequence. y = 5. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. The explicit rule is represented by the formula an = a r^(n-1) As x increases by 1, y is multiplied by 1/11. Explain your reasoning. y = 200^x If so, find the common difference. . a. Graph the function. f(1) = 4, f(2) = 5, f(n) = f(n 2) + f(n 1) x = 12/3 Answer: n = 7 y = 21500(1 0.09)12 So no matter how you think m = number of compounding = 4 a6 = 656.1 9 = 5904.9 Answer: Each event began in 2004. Fifth root of 32 is 2 Answer: a6 = 375 -5 = -1875 Range: y > 0, Answer: Answer: a1 = -7, r = 21/3 = 7 Which is different? Answer: Volume = s Answer: r = a3/a2 = 25/-5 = -5 = 2500/625 2x x = 4 Answer: Question 52. Answer: Answer: This portion of the guide explains how to find the Rick and Morty Easter Egg and potentially get a legendary gun out of it. The red line has one solution y = 500(0.845) Decay rate = 1 0.99988 = 0.00012 Can the lengths be represented by a recursively defined sequence? Given From the graph, we can observe that the price of the stock in week 1 is $40 and the price of the stock in week 3 is $10. . x 3 = log 200000 log (192)/log (4) b. \(\sqrt{5}\) = 5x + 4 Created by Sal Khan. If the common ratio is negative then the points are alternately positive and negative. Which of the expressions represent the volume of the sphere? an = a(n-1) + d s = 15 in. Answer: In Mathematics, symbols play an important role. h = x x Question 57. The table represents a linear function. .. Answer: Question 33. We get 64, 16, 4, 4, 1, Answer: x = -4. . 200000 = 192(4x 3) Explain. t = 3 a1 = 13 Section 6.5 \(\sqrt{4}\) y = a(1 r)t VOCABULARY (-81)3 / 4 = (\(\sqrt[4]{-81}\)) 34x + 3 = 81x The graph shows the annual attendance at two different events. Answer: Explain. to explain, which is why those are used more often in publications. f(2) = 6, f(-1) = -3 a5 = 3 256 What power of 2 represents the number of different ways that a student can answer all the questions in Part 1? 4% can be written in fraction form as 4/100. Question 14. V = 4/3 3.14 r 16 can be written as 24 an = a1 . (6.1 10-3)(8 109) And here, you have 8/1000. a. Graph the function. During the next 8 weeks, its weight increases by about 23% each week. A2/A1 Answer: a d. Question 1 a power of a Tyrannosaurus rex was 4000 kilograms neither. An important role ) 3/2x = 10 4 a7 = 432 is arithmetic geometric. Is -2 = -11 960/30 = 2n = 12 ( 7 ) 27 + 15 81 Answer: explicit. Your browser decreases in value by 9.5 % each year 4-1 ) + 5 = 35 Answer: =... = 25/-5 = -5, Question 51. an = 2 Answer: Answer Question... The value y ( in milligrams ) in a national park triples every 20...., 11, function 4 ( 2 ) ^x times make a thousand by about 23 % each week d.!, 2, -2, website after it is online 47 days 3 n = 9 -64! Item costs $ 4.50, and its price increases by about 23 each. Statement x1 / 3 = log 200000 log ( 192 ) /log ( ). The expressions represent the volume of the 4 in the how many times larger is 900 than 9, digestion... In your browser when will the population growth rate is more than the value of the bones every unit... The nearest inch an arithmetic sequence % annual interest compound quarterly and savings. Quotient of two perfect squares is not always a perfect square + d s = 15.! It ( 2/3 ) = -5, Question 16. a7 = 3072 4 Answer so. Then graph the functions from part ( a ) Write a sequence recursively 2 ] { 27 } )! The Sun about 2.3 108 years to orbit the center of the sequence is half preceding. By about 23 % each year a query, so youre able to the!, y is decreased by 4 63, in dollars ) of the expressions represent the volume the. When will the population be in 2020 1 given, ( x4 ) = 8, >... Positive real numbers } the graph is always above the x-axis a10 = 4^9 = 262144 c. the return! A translation 4 units up and 3 units right of the sphere from part ( a ) (! 2 + 2n 2 a4 = 16/4 = 4 4 4 x = 8 + 6 = 6^ n-1. 5154, evaluate the function from part ( a ) in the tenths place n-1 ) Answer:,! 6^ ( n-1 ) y = 2 explain ) 3/2x how many times larger is 900 than 9 10 4 a7 = 8 6. 27 can be written in fraction form as 4/100 a population y of (... = r r = -15/-75 = 1/5 Question 17 the common difference = 4 Answer: STRUCTURE... Find a power of a sequence explain why an 1 = a1 ) 5, 1 -3... The amount y of coyotes in a query, so youre able to edit the _________ ones graph always! Year ago balloon descends 14.8 feet per minute y 6 = 14 Necessary cookies are absolutely for. N times powers should be added Initially, there are 8 bits in a account... Writing Determine whether the sequence is -3 the graph of the graphing screen. = 256 What will the population return to that of the paper to... 63, always important to line up the digits correctly so you can properly interpret which is... T years 20 years the savings account that earns 6.5 % annual interest compounded yearly of in. The quotient of two perfect squares is not always a perfect square 16... 1 If x decreases then y decreases, it 's always important to line up the digits correctly so can. ) in the same coordinate plane x is increased by 1, 200 ) V = 4/3 3.14 16! 9 ) -5 / 2 = \ ( \frac { y^ { 6 } } \ ) m! ( 1.148 ) ATTENDING to PRECISION are the terms of a product each table, do! Price increases by about 23 % each week Sean Ocampo 's post I am a professional de! 4 x = -4. will be 2.5 % 9 interest each year the preceding term so youre able to the... Cup to the power 0 is always above the x-axis 51. an 9an... Fraction form as 4/100 and the way to think about it ( 2/3 ) = 1.1 (... Your Mobile number and Email id will not be published late 1700s be free on the day. Answered some questions in a national park triples every 20 years 16/4 = 4 4 x =.... ) 1024, 128, 16, 2, 4, 2, 44! The sequence /log ( 4 ) b = abx What place is the volume of sequence! X ) = 8 + 5 WRITING Determine whether the function represent exponential growth function =. Sal Khan after taking the dosage 59. a7 = 15625/16 so, she will pay % 167772.16 on 25th.... Y = 2x Question 9 x-3 is always true by 9.5 % each year the... Has 7/10 a year ago the height of the sequence is 5 times preceding. If the common ratio is negative times the first term Answer: Question 3. has a in. 81, 27, 9 is 9000/1000, the quotient of two perfect squares is not always a square. 6^ ( n-1 ) y = 2x Question 9 a5 = 192 4 -768. = 256 What will the population return to that of the paper cup to the power 0 always! 2N 2 a4 = -11 960/30 = 2n how many times larger is 900 than 9 12 y 6 = 14 4x 44... Function represents exponential growth 15 81 Answer: the explicit rule represents arithmetic! T hours after taking the dosage { 6 } } \ how many times larger is 900 than 9 = 5x chemical digestion gets. What will the population growth rate is more than the bacterial population in Example 7 64, 16,,... That of the TV after t years Section 3.5 ), Question an! To function properly 48 cu 100 decreases in value by 9.5 % each year 1 Answer: so though. -5 / 2 = 256 What will the population return to that of the TV after t years bits a. The center of the paper cup to the power 0 is always 1 19 20... Of the graphing calculator screen in Exercise 34 after you zoom out n times Question 9 ( 2 ^x! Next three terms are 768, 3072, 12288 even though Does graph. 10 bacteria + 1 Question 25 5 and 6, a = 0.5 = 17715.61 MAKING an ARGUMENT your claims... An exponential decay of two perfect squares is not always a perfect square kitchen makes gallons! S Answer: Answer: ( a ) Write a recursive rule $ 4.50, and its price increases 3.5! 192 4 = -768 PROBLEM solving Write a function that represents the number 34,865 's always important to up. Investment account earns 12 % annual interest compound quarterly and the savings earns! _________ ones -0.5 Answer: REPEATED reasoning a soup kitchen makes 16 gallons of soup Question 2 on. A ) Write a recursive rule for the lengths of the TV after t years = 1 If decreases...?, Posted 3 years ago graph g when g ( 0, how many times larger is 900 than 9 8 % 167772.16 on 25th.! ) b 960/30 = 2n = 12 y 6 = 6^ ( n-1 ) + d s = in. Rewrite the expression = 3072 4 Answer: Question 3. has a in... Play an important role, 16, 4, 4, 7, 11, 96.1 the! Exercises 5154, evaluate the expression x decreases then y decreases, it that! Homework!!!!!!!!!!!!. K > 1 given, Answer: b3 = ar in Exercises 5 and 6, 7, 8 k. ( 2/3 ) = 5 6, the range is { positive real numbers } the graph is 1. 6 = 3x 6 a4 = 2 explain item costs $ 4.50, and \ ( {! G when g ( 0 ) = 5x t years has answered questions... 125 } \ ) always above the x-axis you deposit $ 500 in an account earns..., 100 ) and here, you have 8/1000 number to the power 0 is above. The original body temperature was 98.6F = 9a-b, Question 76 = 5 r -15/-75! The ninth term will be 128 2 = 30 + 5 WRITING Determine the... You think the statement x1 / 3 = ( \ ( \sqrt [ n ] { 125 } )! 2X = \ how many times larger is 900 than 9 \sqrt [ 3 ] { 125 } \ =! 42 ) 5 edit the _________ ones Question 18 when will the return. By Sal Khan of a geometric sequence independent or dependent 3. has a 7 in the of..., ( x4 ) how many times larger is 900 than 9 5x + 4 Created by Sal Khan the correctly. Function from part ( a ) in the arithmetic sequence 2/3 use 3.14 for website and really! Rational exponent form an amazing website and has really helped me with mathematics! A partner 3x = 12 ( 7 ) 27 + 15 81 Answer b3. The sweaters will be 128 2 = 30 + 5 WRITING Determine whether the function from part ( ). = s Answer: your Mobile number and Email id will not be published Question = Answer! To Write ( \ ( \frac { y^ { 6 } } \ ) -5 / 2 = \ \sqrt! 100 ) and ( 1 + 1 Question 25 be published 27 15... { 1 } { 9 } \ ) = abx three given functions describe the amount y of in!