Math 3201 Chapter 6 Review Name:

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1 Math 01 Chapter 6 Review Name: Multiple Choice 1. Which of the following is an exponential function? A. f(x) = x B. g(x) = ( 1) x C. h(x) = 17 x D. j(x) = x. Match the following graph with its function x A. = (0.5) x B. = (1.5) x C. = 0.5() x D. = (0.75) x. Match the following graph with its function x A. = (0.5) x B. = (1.5) x C. = 0.5() x D. = (0.75) x 4. Identif the range of the exponential function = 10 x. A. { < 0, R} B. { > 0, R} C. { 0, R} D. { R}

2 _ 5. Determine the -intercept of the exponential function f(x) =. A. 0 B. 1 C. D Which option best describes the behaviour of the exponential function f(x) =? A. increasing because a > 1 B. decreasing because 0 < a < 1 C. increasing because b > 1 D. decreasing because 0 < b < 1 7. Express as a power with a base of. A. B. C. D. 8. Express as a power with a base of. A. B. C. D. 9. Solve the following exponential equation b writing both sides with the same base. A. x = B. x = C. x = 4 D. x = Solve the following exponential equation b writing both sides with the same base. A. z = 7 B. z = 8 C. z = 9 D. z = The population of a specific bacteria growing in a Petri dish is modelled b the function, where P(t) represents the number of bacteria and t represents the time, in das, after the initial time. How long does it take for the population to double? A. 1 da B. das C. das D. 9 das

3 _ 1. The following data set involves exponential growth. Determine the missing value from the table. x A. 6.5 B C D Determine the equation of the exponential regression function for the data. x A. = 75(0.8) x B. = 75(1.6) x C. = 60(0.8) x D. = 60(1.6) x 14. A scatter plot is drawn using a data set x Identif the equation of the curve of best fit. A. = 1(1.) x B. = 1(0.) x C. = 4(1.5) x D. = 4(0.5) x 15. The equation of the exponential function that models a data set is = 6.8(1.0) x. Determine the range of this function. A. { > 0, R} B. { R} C. { > 6.8, R} D. { > 1.0, R} 16. An investment can be modelled b the following growth function, where x represents the time in ears: = 500(1.018) x. What was the principal invested? A. $150 B. $500 C. $18 D. $1018

4 17. An investment can be modelled b the following growth function, where x represents the time in ears: = 500(1.018) x. What was the annual interest rate for the investment? A. 5% B % C. 18% D. 1.8% 18. Eli invested $1000 at %/a compounded quarterl. Define an exponential growth function for this investment in the form A(n) = P(1 + i) n where n represents the number of compounding periods. A. A(n) = 1000(1.00) n B. A(n) = 1000(1.0075) n C. A(n) = 1000(1.0) n D. A(n) = 4000(1.0) n 19. Denis recentl spent $180 on a new laptop for his home business. He read that the depreciation rate for this model laptop is 5%. How much mone should Denis expect to sell his laptop for in three ears? A. $540 B. $960 C. $0 D. $ Solve the following exponential equation b writing both sides with the same base. 1. A research lab has a 1 mg sample of a radioactive substance. The amount of the substance, A(t), left in the sample can be modelled b the half-life function where t represents the time, in das, after the initial time. How long does it take for the sample to reduce to one quarter its initial amount?. Determine whether the following data set involves exponential growth, exponential deca, or neither. Explain how ou know. x The fish population in Loon Lake is modelled b the equation P(t) = 500(0.9) t where P(t) represents the number of fish and t represents the time, in ears, since 010. Estimate the fish population in Complete the table of values for a $50 investment earning.5%/a compounded monthl. Time (months) 0 1 Value ($) Nina invested $000 at 1.%/a compounded weekl. Define an exponential growth function for this investment in the form A(n) = P(1 + i) n, where n represents the number of compounding periods.

5 6. A vehicle was purchased for $ in 005. The book value of the vehicle can be modelled b the exponential function where represents the value in dollars and x represents the time, in ears, after 005. a) How does the value of the vehicle change over time? Explain how ou know. b) Estimate the value of the vehicle in 015. Show our work. 7. Use what ou know about the exponential function to predict the number of x-intercepts, the -intercept, the end behaviour, increasing or decreasing, the domain, and the range of the following functions: a) 1 x b) x 4 8. Solve the equation and verif our answer b substitution. Show our work. 9. Solve the equation and verif our answer b substitution. Show our work. 0. Thorium-7 has a half-life of 18.4 das. The remaining amount of a 50-mg sample of thorium- 7 can be modelled b the equation where A(t) is the amount of thorium-7 remaining, in milligrams, and t is the time in das. Determine the amount of thorium-7 remaining after 10 das, to the nearest milligram. Show our work bi-weekl paments are required to pa off a loan. How man ears does this represent?. A student repaid a total of $9.6 for a loan including the principal and interest. If the interest rate was 6% compounded monthl for ears, what was the principal amount of the loan, to the nearest dollar?. Karen is going to invest $ She has options: A. 7%/a compounded annuall for ears B. 6%/a compounded monthl for ears Which option should she choose? Explain. 4. Zachar borrowed $500 at a rate of 8% compounded semi-annuall for ears. How much interest will be charged for borrowing the mone? x 6 5. Solve for x : a) 1 x b) 5 x The amount of a substance, A(t), left in a sample is modeled b A( t) A0, where t represents the time, in weeks, after the initial time. If there are 5 mg remaining after 6 das, how much was present initiall? t