Name:_________________________________
Date:__________ Period:__________
Algebra 2 Chapter 8 Test
You must show all WORK and REASONING to receive full credit!
Evaluate each function to the nearest hundredth for x = -2, -1, 0, 1, and 2.
Use a table and graph each function.
1. y  3(2) x
1
2. y  4 
2
x
Write an exponential function of the form y  ab x that includes the given points.
3. (1, 2), (2, 6)
4. (2, 122.5), (3, 857.5)
5. You put $2000 into an account earning 4% interest compounded continuously. Find the amount after 8
years.
Name:_________________________________
Date:__________ Period:__________
Use the Change of Base Formula to rewrite each expression using common logarithms (base 10) and
evaluate.
6. log 4 12
7. log 2 8
Evaluate each logarithm. SHOW ALL WORK AS WE LEARNED IN CLASS!
1
8. log 5 125
9. log 1
10. log 3 729
4
2
Write each equation in logarithmic form.
12. 7 3  343
13. 2 4  0.0625
Write each logarithmic expression as a single logarithm.
14. log 2 x  3 log 5  log z
15. 2 log 2 a  3 log 2 b
Expand each logarithm.
16. log 5 6 x
17. log 5
x2 y
z4
11. log 9
1
3
Name:_________________________________
Date:__________ Period:__________
For Problems 21 and 22: a) condense the logarithmic expression; b) evaluate
18. log 5  log 10  log 2
19. log 8 256  log 8 4
Solve each equation. Round to the nearest hundredth.
20. log 5 x  3
21. 10 2 x  40
23. log 5 (3x  10)  3 log 5 4  2
24. 2 ln 3x 2  18
22. e 2 x4  16
25. 2  8 x1  14
26. A parent raises a child’s allowance by 15% each year. If the allowance is $3 now, when will it reach $21?
Name:_________________________________
Date:__________ Period:__________
27. Hg-197 is used in Kidney scans. It has a half-life of 64 hours.
a) Write the exponential decay function for a 12-mg sample.
b) Find the amount of Hg-197 remaining after 96 hours.
28. You put $3000 into an account earning interest compounded continuously. After 6 years, you have
$4049.58.What percent interest did you earn? Show your work algebraically!
True/False: Carefully consider each problem and indicate whether it is true of false. IF FALSE,
EXPLAIN YOUR ANSWER!!!
29. The following equation indicates that you have an initial amount of 20 and it is growing by 16 percent each
year (assume that x is measured in years): y  200.16x
30. log x  y   log x  log y
31. If x log 8  log 43 , then 8x = 43.
32. Natural logarithms follow the same rules as other types of logarithms.
33. The value of a car depreciates 38% each year. If its initial value is $17,000, then the following equation
models its value over time (assume x is measured in years): y  17,0000.72x