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Pre-Test Name Date 1. The formula for an account that earns simple interest is Pt 5 P0 1 (P0 ? r)t where Pt represents the balance in the account after t years, P0 represents the initial deposit, and r represents the interest rate. The formula for an account that earns compound interest is Pt 5 P0 ? (1 1 r)t where Pt represents the balance in the account after t years, P0 represents the initial deposit, and r represents the interest rate. a. Complete the table below for an initial deposit of $20,000 at a rate of 2.5%. Round each amount to the nearest dollar. Time 6 months 1 year 5 years 20 years Simple Interest Balance Compound Interest Balance b. Determine the rate of change for each function. Show your work or explain your reasoning. © 2012 Carnegie Learning 5 c. Compare the rates of change. What does this tell you about the graphs of the functions? Explain your reasoning. Chapter 5 Assessments 8047_Assess_Ch05.indd 895 895 20/04/12 12:58 PM Pre-Test page 2 2. Identify each of the following for the function f(x) 5 3 ? 4x. Then graph the function. a. x-intercept(s) b. y-intercept c. asymptote d. domain e. range f. interval(s)of increase/decrease 3. Write the equation of each function after the translation described. a. f(x) 5 210x after a translation 5 units to the right b. g(x) 5 3x after a translation 4 units up c. h(x) 5 2x2 after a translation 2 units left and 1 unit down 4. Describe each graph in relation to its basic function. 5 b. Compare f(x) 5 bx 1 1 to the basic function h(x) 5 bx. © 2012 Carnegie Learning a. Compare f(x) 5 (x 1 3)2 to the basic function h(x) 5 x2. c. Compare f(x) 5 b–x to the basic function h(x) 5 bx. 896 Chapter 5 Assessments 8047_Assess_Ch05.indd 896 20/04/12 12:58 PM Pre-Test page 3 Name Date 5. Write each expression in rational exponent form. 3 a. 10 4 b. d 6. Write each expression in radical form. __ 1 a.112 __ 1 b.a5 7. Solve each exponential equation for x. a. 5x 1 3 5 15,625 1 5 4,096 b. ____ 4x21 © 2012 Carnegie Learning 5 Chapter 5 Assessments 8047_Assess_Ch05.indd 897 897 20/04/12 12:58 PM © 2012 Carnegie Learning 5 898 Chapter 5 Assessments 8047_Assess_Ch05.indd 898 20/04/12 12:58 PM Post-Test Name Date 1. The formula for an account that earns simple interest is Pt 5 P0 1 (P0 ? r)t where Pt represents the balance in the account after t years, P0 represents the initial deposit, and r represents the interest rate. The formula for an account that earns compound interest is Pt 5 P0 ? (1 1 r)t where Pt represents the balance in the account after t years, P0 represents the initial deposit, and r represents the interest rate. a. Complete the table below for an initial deposit of $10,000 at a rate of 1.5%. Round each amount to the nearest dollar. Time 6 months 1 year 5 years 20 years Simple Interest Balance Compound Interest Balance b. Determine the rate of change for each function. Show your work or explain your reasoning. © 2012 Carnegie Learning 5 c. Compare the rates of change. What does this tell you about the graphs of the functions? Explain your reasoning. Chapter 5 Assessments 8047_Assess_Ch05.indd 899 899 20/04/12 12:58 PM Post-Test page 2 2. Identify each of the following for the function f(x) 5 24 ? 2x. Then graph the function. a. x-intercept(s) b. y-intercept c. asymptote d. domain e. range f. interval(s) of increase/decrease 3. Write the equation of each function after the translation described. a. f(x) 5 5x after a translation 3 units to the left b. g(x) 5 2x after a translation 6 units down c. h(x) 5 4x2 after a translation 5 units right and 3 units up 4. Describe each graph in relation to its basic function. 5 b. Compare f(x) 5 (b 2 2)x to the basic function h(x) 5 bx. © 2012 Carnegie Learning a. Compare f(x) 5 x2 2 7 to the basic function h(x) 5 x2. c. Compare f(x) 5 2bx to the basic function h(x) 5 bx. 900 Chapter 5 Assessments 8047_Assess_Ch05.indd 900 20/04/12 12:58 PM Post-Test page 3 Name Date 5. Write each expression in rational exponent form. 4 a. 6 3 2 b. x 6. Write each expression in radical form. __ 1 a.73 __ 1 b.69 7. Solve each exponential equation for x. a. 34x 5 531,441 b. 5x 1 1 5 ____ 1 625 © 2012 Carnegie Learning 5 Chapter 5 Assessments 8047_Assess_Ch05.indd 901 901 20/04/12 12:58 PM © 2012 Carnegie Learning 5 902 Chapter 5 Assessments 8047_Assess_Ch05.indd 902 20/04/12 12:58 PM Mid-Chapter Test Name Date 1. Using coordinate notation, write the function f(x) = x – 3 as a vertical translation. 2. The formula for an account that earns compound interest is Pt 5 P0 ? (1 1 r)t, where Pt represents the balance in the account after t years, P0 represents the initial amount of the deposit, and r represents the interest rate. Carrie is considering depositing $1,480 into an account that pays compound interest. How much will be in her account in each situation? Round to the nearest cent. a. 1.9% for ten years b. 3.6% for fifteen years 3. Write the equation of each function after the translation described. a. f(x) 5 x after a translation 1 unit down 5 b. g(x) 5 x after a translation 2 units up © 2012 Carnegie Learning 3 c. h(x) 5 x2 after a translation 2 units left and 5 units down 4. The revenue for a company this year was $750,000. Each year the revenue increases at a rate of 0.75% per year. Write a function that represents the company’s revenue as a function of time in years. Chapter 5 Assessments 8047_Assess_Ch05.indd 903 903 20/04/12 12:58 PM Mid-Chapter Test page 2 5. Write a statement that correctly compares the y-intercepts of the functions g(x) 5 x3 1 8 and h(x) 5 x3 2 8. 6. Write the function f(x) 5 9x 2 2 after each vertical translation. a. 4 units down b. 8 units up 7. The formula for an account that earns simple interest is Pt 5 P0 1 (P0 ? r)t, where Pt represents the balance in the account after t years, P0 represents the initial deposit, and r represents the interest rate. Gregory deposits $900 into an account that earns 1.5% simple interest annually. How much will be in his account after one year? ( ) x 8. What is the range of the function f(x) 5 __ 2 1 2? 3 9. What is the y-intercept of the function f(x) 5 0.4x 1 2? 5 10. Describe each graph in relation to its basic function. b. Compare f(x) 5 (b 2 1)x to the basic function g(x) 5 bx. © 2012 Carnegie Learning a. Compare f(x) 5 x3 1 9 to the basic function g(x) 5 x3. c. Compare f(x) 5 (x 2 1)2 2 2 to the basic function g(x) 5 x2. 904 Chapter 5 Assessments 8047_Assess_Ch05.indd 904 20/04/12 12:58 PM Mid-Chapter Test Name page 3 Date 11. Write the equation for the line that represents the horizontal asymptote of each function. a. f(x) 5 25x b. f(x) 5 16(1 1 0.5)x 1 3 12. The expenses for a company this year were $74,000. Write a function that represents the company’s expenses as a function of time in years for each situation. a. expenses increase at a rate of 2.3% per year b. expenses decrease at a rate of 1.7% per year © 2012 Carnegie Learning 5 Chapter 5 Assessments 8047_Assess_Ch05.indd 905 905 20/04/12 12:58 PM © 2012 Carnegie Learning 5 906 Chapter 5 Assessments 8047_Assess_Ch05.indd 906 20/04/12 12:58 PM End of Chapter Test Name Date 1. Carlos has been collecting baseball cards for the past few years. The number of total cards in his collection each year is as follows. • 50 cards the first year • 100 cards the second year • 150 cards the third year • 200 cards the fourth year Write a function that represents the number of cards as a function of the number of years, t. ( ) x 2. Identify each of the following for the function y 5 __ 1 . 3 a. x-intercept(s) b. y-intercept c. asymptote d. domain e. range f. interval(s) of increase/decrease 3. Kendra graphed the function f(x) 5 9x. a. Write a function that is a reflection of the function about the vertical line x 5 0. 5 © 2012 Carnegie Learning b. Write a function that is a reflection of the function about the horizontal line y 5 0. 4. Write each fraction as a single power. 1 a. _______ 10,000 1 b. __________ 1,000,000 Chapter 5 Assessments 8047_Assess_Ch05.indd 907 907 20/04/12 12:58 PM End of Chapter Test page 2 5. Write the equation of each function after the translation described. a. f(x) 5 2x after a translation 6 units up b. g(x) 5 __ 1 x3 after a translation 7 units down 2 6. Describe each graph in relation to its basic function. a. Compare f(x) 5 (x 2 2)3 – 1 to the basic function g(x) 5 x3. b. Compare f(x) 5 2x2 to the basic function g(x) 5 x2. 7. Write each expression in radical form. __ 1 __ 7 a.83 b.c8 __ 1 c.15d4 2 __ d.(9g)5 8. Using coordinate notation, write each function as a vertical translation. a. f(x) 5 x 1 1 b. f(x) 5 x 2 7 9. Malea bought the following numbers of stickers each day. 5 • one sticker on the first day • sixteen stickers on the third day • sixty-four stickers on the fourth day Write a function that represents the number of stickers as a function of the number of days, t. 10. Write each expression in rational exponent form. 908 ___ 5 a. 3 b.√10 7 c. 46 1 3 5 d. x © 2012 Carnegie Learning • four stickers on the second day Chapter 5 Assessments 8047_Assess_Ch05.indd 908 20/04/12 12:58 PM End of Chapter Test page 3 Name Date 11. The velocity v in meters per second (m/s) of a free-falling object that has fallen h meters is given _______ by the equation v 5 √ 2(9.8)h . If an object is dropped from a height of 75 meters, what is the velocity of the object when it hits the ground? Round to the nearest tenth. 12. Solve each exponential equation for x. a. 5x 2 2 5 3,125 1 b. 322x 5 ____ 729 1 5 216 c. _____ 6x 1 2 1 5 ______ d. _____ 1 7x 2 1 2,401 13. The expenses for a company this year were $125,000. The expenses have been increasing at a rate of 3.5% per year. Write a function that represents the company’s expenses as a function of time in years. © 2012 Carnegie Learning 5 Chapter 5 Assessments 8047_Assess_Ch05.indd 909 909 20/04/12 12:58 PM © 2012 Carnegie Learning 5 910 Chapter 5 Assessments 8047_Assess_Ch05.indd 910 20/04/12 12:58 PM Standardized Test Practice Name Date 1. The formula for an account that earns simple interest is Pt 5 P0 1 (P0 ? r)t, where Pt represents the balance in the account after t years, P0 represents the initial deposit, and r represents the interest rate. Paul deposited $500 into an account that earned 4% simple interest annually. How much was in his account after one year? a. $20 b. $480 c. $520 d. $540 2. Which represents the function f(x) 5 x 1 1 as a vertical translation one unit up using coordinate notation? a. (x, y 2 1) b. (x, y 1 1) c. (x 2 1, y) d. (x 1 1, y) 3. The profit for a company this year was $100,000. Each year the profit increases at a rate of 1.2% per year. Which function shows the company’s profit as a function of time in years? a. f(t) 5 100,000 ? 0.012t b. f(t) 5 100,000(1 1 1.2)t c. f(t) 5 100,000(1 1 0.012)t d. f(t) 5 100,000 ? 1.2t 4. What is ____ 1 written as a single power? 100 a. 1023 5 b. 1022 © 2012 Carnegie Learning c. 102 d. 103 5. Which shows the function f(x) 5 2x4 after a horizontal translation 2 units left? a. f(x) 5 2x4 1 2 b. f(x) 5 2x4 2 2 c. f(x) 5 2(x 1 2)4 d. f(x) 5 2(x 2 2)4 ( 4 ) x 6. What is the range of the function f(x) 5 __ 1 ? a. x , 0 b. x . 0 c. f(x) , 0 d. f(x) . 0 Chapter 5 Assessments 8047_Assess_Ch05.indd 911 911 20/04/12 12:58 PM Standardized Test Practice page 2 7. The graph of f(x) 5 x3 is shown. Which shows 2f(x)? y 8 6 4 2 0 28 26 24 22 2 4 6 8 x 22 24 26 28 b. y y 8 8 6 6 4 4 2 2 0 28 26 24 22 2 4 6 8 x 8 2 4 6 8 x 28 28 912 6 26 26 y y d. 8 8 6 6 4 4 2 2 0 28 26 24 22 4 24 24 c. 2 22 22 5 0 28 26 24 22 2 4 6 8 x 0 28 26 24 22 22 22 24 24 26 26 28 28 x © 2012 Carnegie Learning a. Chapter 5 Assessments 8047_Assess_Ch05.indd 912 20/04/12 12:58 PM Standardized Test Practice page 3 Name Date 8. Which correctly compares the y-intercepts of the functions a(x) 5 x2 1 2 and b(x) 5 x2 2 2 to the basic function c(x) 5 x2? a. The y-intercept of a(x) 5 x2 1 2 is 2 units below the y-intercept of the basic function. The y-intercept of b(x) 5 x2 2 2 is 2 units below the y-intercept of the basic function c(x). b. The y-intercept of a(x) 5 x2 1 2 is 2 units above the y-intercept of the basic function. The y-intercept of b(x) 5 x2 2 2 is 2 units above the y-intercept of the basic function c(x). c. The y-intercept of a(x) 5 x2 1 2 is 2 units above the y-intercept of the basic function. The y-intercept of b(x) 5 x2 2 2 is 2 units below the y-intercept of the basic function c(x). d. The y-intercept of a(x) 5 x2 1 2 is 2 units below the y-intercept of the basic function. The y-intercept of b(x) 5 x2 2 2 is 2 units above the y-intercept of the basic function c(x). 9. What is the solution to the exponential equation ___ 1 5 2x 1 1? 64 a. x 5 27 b. x 5 26 c. x 5 25 d. x 5 5 10. Which is a reflection of the function f(x) 5 23x about the horizontal line y 5 0? a. g(x) 5 232x b. g(x) 5 32x c. g(x) 5 23x d. g(x) 5 3x 5 11. Thomas counts the number of cars he sees in the parking lot of the school each hour of the day. He counted the following number of cars the first four hours of the day. © 2012 Carnegie Learning • 12 cars the first hour • 24 cars the second hour • 36 cars the third hour • 48 cars the fourth hour. Which function represents the number of cars as a function of the number of hours, h? a. f(h) 5 12h b. f(h) 5 12(h 2 1) c. f(h) 5 12h d. f(h) 5 12h 2 1 Chapter 5 Assessments 8047_Assess_Ch05.indd 913 913 20/04/12 12:58 PM Standardized Test Practice page 4 12. The average attendance at a local high school this year was 950 students. Each year the attendance decreases at a rate of 0.5% per year. What will the average attendance be in three years? a. 945 b. 941 c. 936 d. 893 3 ? 13. What is 64 a. 3 b. 4 c. 21 d. 192 14. Which shows the function f(x) 5 7x after a vertical translation 4 units down? a. g(x) 5 7x 1 4 b. g(x) 5 7x 2 4 c. g(x) 5 4x 1 7 d. g(x) 5 4x 2 7 15. Taylor earned the following amount each day. • one dollar of the first day • three dollars on the second day • nine dollars on the third day • twenty-seven dollars on the fourth day 5 Which function represents Taylor’s daily earnings as a function of the number of days, t. a. f(t) 5 3t c. f(t) 5 3t 2 1 d. f(t) 5 3t 16. What is the equation for the line that represents the horizontal asymptote of the function f(t) 5 25,000(1 1 0.025)x? a. x 5 0 b. y 5 0 © 2012 Carnegie Learning b. f(t) 5 3t 1 1 c. x 5 25,000 d. y 5 25,000 914 Chapter 5 Assessments 8047_Assess_Ch05.indd 914 20/04/12 12:58 PM Standardized Test Practice Name page 5 Date 17. What is the solution to the exponential equation 81 5 3x 2 1? a. x 5 23 b. x 5 3 c. x 5 4 d. x 5 5 18. The formula for an account that earns compound interest is Pt 5 P0 ? (P0 1 r)t, where Pt represents the balance in the account after t years, P0 represents the initial deposit, and r represents the interest rate. Brenda deposited $225 into an account that earns 7.25% compound interest. How much will be in her account after six years? Round to the nearest cent. a. $342.43 b. $241.31 c. $231.44 d. $16.31 19. Which equation has the following four characteristics? • is an exponential function. • is continuous. • is increasing. • is translated 5 units up from f(x) 5 3x. a. g(x) 5 3x 1 5 5 b. g(x) 5 3x 2 5 c. g(x) 5 3x 1 5 © 2012 Carnegie Learning d. g(x) 5 3x 2 5 20. The velocity v in meters per second (m/s) of a free-falling object that has fallen h meters is given _______ by the equation v 5 √ 2(9.8)h . If an object is dropped from a height of 62 meters, what is the velocity of the object when it hits the ground? Round to the nearest tenth. a. 4.4 m/s b. 11.1 m/s c. 34.9 m/s d. 1215.2 m/s Chapter 5 Assessments 8047_Assess_Ch05.indd 915 915 20/04/12 12:58 PM © 2012 Carnegie Learning 5 916 Chapter 5 Assessments 8047_Assess_Ch05.indd 916 20/04/12 12:58 PM