Algebra 2
Review Chapter 8
Name ______________________________
Evaluate each function to the nearest hundredth for x = -2, -1, 0, 1, and 2. Graph each function. Show your table.
1. y = 2(4)x
2. y = 0.2(3.8)x
Write an exponential function of the form
y  ab x that includes the given points.
3. (1, 1) and (2, 3)
4. (3, 1.5) and (4, 15)
5. Find the amount in a continuously compounded account for the given conditions.
Principal: $1000
Rate: 4.8%
Time: 2 years
Describe how the graph of each function is related to the graph of its parent function.
6.
y  3 x  1
y  8x 1
7.
8.
y  2 x 1  3
Use the Change of Base Formula to rewrite the expression using common logarithms.
9.
log 3 16
Evaluate each logarithm.
10.
log 2 64
11. log 3
1
9
12. log 0.00001
13.
log 2 1
Graph each logarithmic function. Show inverse and tables.
14. y  log 3 x
Write each equation in logarithmic form.
15. 62 = 36
16. 2-3 = 0.125
Write each logarithmic expression as a single logarithm.
17. 4 log x  log 7
18. log z  log y
Expand each logarithm.
19.
log x 2 y 3
20. log 3
2
x
Write each expression as a single natural logarithm.
21.
ln 3  5 ln 3
Use the properties of logarithms to evaluate each expression.
23. log 1  log 100
24. 2 log 3 3  log 3 3
22. ln a  2 ln b 
25.
1
ln c
2
log 6 4  log 6 9
Solve each equation. Round to the nearest hundredth.
26.
log x  log 3  8
29. 3
x 1
 24
27.
1
log x  log 4  2
2
30. 2 log x  4
28. 4  27
x
31. ( 34 )  81
x
Use the properties of natural logarithms to simplify each equation and solve it. Round to the nearest hundredth.
32.
3 ln x  ln 5  7
33. 4e(x-1) = 64
34. ln( 4 x  1)  36
35. A new college graduate’s income increases by 8% each year. The first salary was $26,000, when will it reach $40,000?
36. One form of radioactive iodine has a half-life of about 8 days.
a. Write an equation hat models the exponential decay of 500g of this form of radio active iodine.
b. How much will be left after 32 days?
Algebra 2
Answers Chapter 8
15.
log 6 36  2
1.
-2
-1
0
1
2
16.
log 2 0.125  3
17.
log 7 x 4
18.
log
2.
-2
-1
0
1
2
.125
.5
2
8
32
z
y
19. 2 log x  3 log y
.01
.05
.2
.76
2.89
1 x
3. y = (3)
3
20.
log 3 2  log 3 x
21. ln
1
81
22. ln
a c
b2
23. 2
4. y = .0015(10)x
24. 1
5. $1100.76
25. 2
6. Reflected and Up 1
7. Down 1
8. Left 1, Up 3
26 3 10
8
27. 625
28. 2.38
log 16
9.
log 3
10. 6
11. -2
12. -5
13. 0
14.
.11
.33
1
3
9
y  3x
-2
-1
0
1
2
29. 3.89
30. 0.01
31. -15.28
32. 6.03
33. 3.77
34. 1.078  10
15
35. approx. 5.4 years
1
36a.
y  500( 12 ) 8
36b. 31.25
x