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Chapter 6: Exponentials Math 3201 Public Exam Review Write the letter of the correct response in the space provided to the left 1. _____ Which statement best describes the exponential function f(x) = 3 1 ? 4 A. Increasing function; y-intercept 3 B. Decreasing function; y-intercept 3 C. Increasing function y-intercept ¾ D. Decreasing function; y-intercept ¾ 2. _____ Which is an increasing exponential function? x A. C. f(x) = 5 1 2 3 x 3 f(x) = (1) 2 x B. f(x) = 1.5(0.5) D. f(x) = 1 5 3 2 x x y 3. _____ Which exponential function best represents the graph? A. B. C. D. 6 x f(x) = 1 4 x f(x) = (4) x f(x) = 4 1 4 x f(x) = 4(4) 4 2 x -2 4. _____ x What is the end behavior of the function y = 2 1 ? 3 A. C. 5. _____ Extends from Q1 to Q2 Extends from Q3 to Q4 A. B. C. D. _____ Extends from Q2 to Q1 Extends from Q4 to Q3 Which statement is true about the table shown below? x (years) y (amount) 6. B. D. -3 5 0 10 3 20 6 40 9 80 12 160 An initial amount of 5 doubles every 3 years An initial amount of 5 triples every 2 years An initial amount of 10 doubles every 3 years An initial amount of 10 triples every 2 years x–2 x–2 = 9 , the graphs of y = 3 To solve the equation 3 and y = 9 were drawn, as shown below. What is the solution to the equation? A. B. C. D. y 0 4 9 there is no solution 10 8 6 4 2 7. _____ Solve for x: 2 A. C. -3 2 3x + 1 =4 2x – 1 -2 B. D. -2 3 2 4 6 x -2 Page 1 of 4 Chapter 6: Exponentials 8. _____ Solve for x: 9 A. _____ Public Exam Review = 3 B. –3 8 –1 2 C. 9. 2x + 1 Math 3201 D. –1 4 1 2 The population growth of a strain of bacteria in a Petri dish is modeled by the t 4 function P(t) = 3000(2) where P(t) represents the number of bacteria after t hours from the initial count. How long will it take for there to be 12000 bacteria? A. C. 10. _____ 4 hours 16 hours a) c) 8 hours 32 hours In the bacteria growth in #9 above, how many will be present 6 hours after the initial count? A. C. 11. B. D. 4762 48000 B. D. 8485 192000 Algebraically solve each equation. Show all necessary workings 9 x+1 = (27) 1 216 2x 2x 4x + 1 =6 b) d) 4(5) x–4 – 25 = 75 2x + 1 7 = 49 Page 2 of 4 Chapter 6: Exponentials 12. Math 3201 Public Exam Review Small rural water systems are often contaminated with bacteria from animals. The number of bacteria present in the tank after t days can be modeled by the function A(t) = 14000(2) t 4 a) How many bacteria are initially present? b) How many days does it take for the bacteria to double? c) Algebraically determine when the number of bacteria will be 224000. 13. Sharon wants to invest $5600 into an account for 7 years. She has the following options: Account #1 has an annual interest rate of 5% compounded quarterly Account #2 has an annual interest rate of 4% compounded semi-annually a) Develop an equation in the form A = P(1 + i) to represent the value of the money in each account and use it to determine how much money would be in each account at 7 years. b) Which account is the best investment option? n Page 3 of 4 Chapter 6: Exponentials Math 3201 Public Exam Review 14. The value of a $47000 car depreciates at a rate of 21% every 2 years. a) Write an exponential function to describe the value of the car over time (t). b) Use the function from part (a) to algebraically determine the value of the car in 15 years. 15. The value of a $157000 house increases by 12% every 4 years. a) Write an exponential function to describe the value of the house over time (t) b) Use the function from part (a) to algebraically determine the value of the house in 25 years Page 4 of 4