Ch. 8 Sections 1 – 6
Practice Test
Name _________________________
Period _____________
1. Determine whether each function represents exponential growth or decay. What is the growth/decay
factor? Find the percent of increase or decrease that the function models.
a) y  61.4
x
b) y  0.20.72 
1
c) y  2.7 
5
x
x
2. Graph the functions.
a) y  3(2)
1
b) y  3 
2
x
x
c) y  2 x3  4
4. Suppose you invest $6,800 at an annual interest rate of 5.2% compounded continuously. Find the
amount you will have in the account after 13 years.
x 8
3
5. Given the function y  0.14   4 . Is the function a stretch, shrink, or neither, and is the
e
function exponential growth or exponential decay. Circle the correct words.
6. Pythag-2 is used to locate brain problems. It has a half-life of 48 days. Write an exponential decay
function for a 80-mg sample. Use the function to find the amount remaining after 100 days.
7. Solve. Round your answers to three decimal places.
a) 6 x  40
b) 50  2(5) x4
c) 32 2 x 3  8 6 x 8
d) 7 x 3  89
f) 2 6 x 3  17  44
e) 114 x 1  56
8. Write in logarithmic form.
a) 9 4  6561
b) 2  4 
1
16
9. Write in exponential form.
a) log 4 4096  6
1
b) log 2    3
8
10. Evaluate each logarithm.
a) log 4 32
b) log 9 243
11. Graph the functions.
a) y  log 3 x
b) y  log 3 x  2
12. Write each logarithmic expression as a single logarithm.
2
a) log 16  log 10  log 3
b) 10 log y  5 log m  log n
3
d) 3 log M  log P  4 log X
c)
1
2
log 144  log 2  log 8
3
3
e) 9 ln x  5 ln 5  8 ln m  4 ln y 
13. Expand each logarithm.
a) log 7 x
4
y
b) log
c2d
4
e
 w6 3 P 

c) log 

K


14. If log 2 5  x and log 2 3  y , rewrite the expression in terms of x and/or y.
3
a) log 2 15
b) log 2  
c) log 2 0.45
5
15. Solve. Round your answers to three decimal places.
a) log 17 x  1  2
b) log 2 8  log 2 5x 2  4
d) log (5 x  12)  3
e) ln 3x  6
c) log 4 8x  log 4 x  3
f) ln 3 x 2  5  2
g) ln  x  1  3
2
 x7
h) ln 
2
 5 
i) 2 ln 5x  ln 6  3
16. Solve. Round your answers to three decimal places.
a) e
x2
 11
b) e
5 x 1
 21
c) e
 x
 
6
 18  52
17. An initial deposit of $6300 is now worth $8073.20. The account earns 3.1% interest and is
compounded continuously. For how long has the money been in the account?
18. If the parent function of an exponential function is f ( x)  6 x , write the equation for this function if it
were stretched by a factor of 3, translated 4 units to the right, and 11 units up.
19. What are two real-world applications of logarithms?