Algebra 2
Study Guide Chapter 8
Name ______________________________
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. Show this on the table. Graph each function.
1. y = 2(4)x
2. y = 0.2(3.8)x
Asymptote:
Write an exponential function of the form
3. (1, 1) and (2, 3)
Asymptote:
y  ab x that includes the given points.
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 (write the sequence of
transformations).
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 and evaluate with a calculator.
9. a) log 3 16
b) log 5
4
Evaluate each logarithm. SHOW ALL WORK AS WE LEARNED IN CLASS!
10.
log 2 64
11. log 3
1
9
12. log 0.00001
13.
log 2 1
Graph the logarithmic function. Fill in AND GRAPH all requested information as you work through the process.
14. y  log 4 x  3  5
Part 1:
Exponential Function:
Table:
x
y
Asymptote:
Part 2: Which line will you reflect the function over to find its inverse?
What is the inverse of the exponential function from Part 1?
What is the asymptote of this inverse function?
Part 3: Write the sequence of transformations needed in order to graph y  log 4 x  3  5 .
What is the asymptote of y  log 4 x  3  5 ?
Write each equation in logarithmic form.
15. 62 = 36
16. 2-3 = 0.125
Write each expression in exponential form.
17. ln 1  0
18. log 8 512  3
19. log 10,000  4
Write each logarithmic expression as a single logarithm.
20. 4 log x  log y  log 7
21. ln x  6 ln z
22.
1
log z  3 log y
2
Expand each logarithm.
23. log x 2 y 3 z 4
24. log 3
2y5
x
Use the properties of logarithms to evaluate each expression.
(A. Condense to one logarithm; B. Evaluate by showing work as we did in class.)
26. log 1  log 100
27. 2 log 3 3  log 3 3

25. ln x

28.
y

z
2
log 6 4  log 6 9
Solve each equation. Round to the nearest hundredth.
29.
ln x  ln 3  2
32.  3 x 1  24
30. 2 log 3 2  log 3 2 x  1  3
31. 2  4 x  29
33. 2 log 2 x  5
34. e 2 x 5  17  35
35. A new college graduate’s income increases by 8% each year. If 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?
37. You invested $200 to an account that compounds continuously with an annual interest rate of 8.2%. After how many years
will the balance in the account be $581 (round to the nearest year)?