Review #15 Exponents and Exponential Functions

Review #15

Name ______Date______Period______Review #15 – Exponents and Exponential Functions

Non- Simplify. Calculator 2x3 Part 1. (-2x3y2)5 2.  8x3

2 1 3. ab-2(ab2 - 3b3) 4. ax  a2x2

3   5  5.   50 6. 2n1/3 (n2/3 + n-1/3)  2 

1 xy3  33 811 7.   8. x3y3 92

1  2 3  3x5y3  c3d 9.   10.  5 3  1  6x y  3 c d3 Answers to Review #15 2 Review #15

2 -  27  3 2 2 1/2 11. −  12. (8 + 6 )  64 

2 1 1 2 3x  3x y 13. a1  b1 14.   1 x2y2

Solve.

3 4 15. 5 16. 2x  3  16 x 3  16

17. 27x = 37· 99 18. 3  27  92x

x 3x 19. 93x    20. 26-x = 42 + x 37

Review #15

Graph each exponential function. Answers to Review #15 3

x4  1  1 21. f(x) =     5 22. f(x) = (4)x − 6  2  2

y y 10 10

2 2 x x -10 -8 -6 -4 -2 2 4 6 8 10 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -2

-4 -4 5x x 23. f(x) = 3 -6  3 24. f(x) = 2e -6 -8 -8 y y 10 10 -10 -10 8 8

2 2 x x -10 -8 -6 -4 -2 2 4 6 8 10 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -2

Write the function-8 for the following graphs. -8 25. ______-10 26. ______-10

y y 10 10 8 Goes through 8 6 (-6, 127) 6 4 4

2 2 x x -10 -8 -6 -4 -2 2 4 6 8 10 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -2

-4 -4 -6 -6 -8 -8

-10 -10 Review Answers to Review #15 4 #15

Formulas will be given on the test. Calculator Part t  1 k At  A0  t 2 A(t) = A0b   nt  r  rt kt A(t) = P1  A(t) = Pe A(t) = A0e  n 

27. There are three options for investing $500. The first, A1(t), earns 7% compounded annually, the second, A2(t), earns 7% compounded quarterly, the third, A3(t), earns 7% compounded continuously. a) Write the function that models b) Find the amount of each each investment. investment after 5 years.

A1(t) = A1(5) =

A2(t) = A2(5) =

A3(t) = A3(5) = c) Graph A3(t) over a 30 year period.

d) When will A3(t) reach $4000?

e) Find the amount that should be invested at 7% compounded quarterly in order to have $2500 in 10 years. Answers to Review #15 5 Review #15

28. The half-life of radioactive cobalt is 5.27 years. a) If 100 grams of cobalt are present now, how much will be present in 15 years?

b) How much was present 5 years ago?

29. Oil is leaking from a tank at a rate of 4% per hour. The tank had 250 gallons of oil when it was full. a) Write a formula for the amount of oil in the tank after t hours.

b) How much oil remains in the tank after 10 hours? What percent of the oil has leaked out at that point?

Mixed Review. Non-calculator. 5x 10 30. Graph fx  31. Graph f(x) = 2(x+4)3 − 2 x3  x2  6x

y y 10 10

2 2 x x -10 -8 -6 -4 -2 2 4 6 8 10 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -2

-10 -10 32. Determine the intercepts of f(x) = x3 + 2x2 – 9x – 18. Answers to Review #15 6

y 15 10 10 1. –32x y 22. Balance 8 c ) 6 4000 2. –1 4 2 3000 x -10 -8 -6 -4 -2 2 4 6 8 10 2 -2 3. a – 3ab 2000 -4

-6 4. a 1000 -8 8 -10 t (years) 5.  5 10 15 20 25 30 y 125 10 22. 6. 2n + 2 8 d) 29.706 years 6 e) $2101.82 7. x2 4 2 28. a) 13.905g 1 1 x b) 193.022g -10 -8 -6 -4 -2 2 4 6 8 10 t 8.  or  -2 29. a) A(t) = 250(.96) 5 243 3 -4 b) 166.208 gallons remain, -6 12 33.5% leaked out 4y -8 30. y 9. -10 10 20 x 8 y 10 6 4 8 3 23. 4 c 6 2 10. x 5 4 3 -10 -8 -6 -4 -2 2 4 6 8 10 d 2 -2 x -4 -10 -8 -6 -4 -2 2 4 6 8 10 16 -2 -6 11.  9 -4 -8 -6 -10 -8 y 12. 10 31. 10 -10 8

13. y 24. 10 6 8 4

6 2 2 2 2 2 x a b a b 4 -10 -8 -6 -4 -2 2 4 6 8 10 or 2 -2 2 2 2 x -4 b  a b  2ab  a -10 -8 -6 -4 -2 2 4 6 8 10 -2 -6 -8 3y -4 -6 -10 14. 2 x y  x -8 32. (-2, 0), (-3, 0), (3, 0), (0, -18) -10 15. 35 x3  1  16. 8, -8 25. f(x) =    2  5  25 x 17. 26. f(x) = 3 − 3 3 t 27. a) A1t  5001 .07 5 4t 18.  .07  A1t  5001  8  4  19. 7, -1 .07t A1t  500e 2 b) $701.28, $707.39, 20. 3 $709.53 21.