TPC out of Blue and Gold Book
Exponential and Logarithmic Review
Name
Pd
UQ: How do we show the relationship between exponentials and logarithms algebraically and graphically?
Covered Concepts:
 Graphing and transforming exponential function graphs
 Exponential growth and decay
 Compound interest
 Continuously compounding interest
 Relationship between exponential and logarithmic functions
 Graphing and transforming logarithmic function graphs
 Simplifying logarithmic expressions
 Solving logarithmic and exponential functions
 Similarities/differences between common logarithms and natural logarithms
1. Suppose you invest $1750 at an annual interest rate of 3.2% compounded continuously. How much will you have in the
account after 6 years?
2. Evaluate the logarithm: log 4 16384 = x
3. Expand the logarithmic expression:
4. Solve log(2𝑥 + 5) = 3.
log 8
𝑚3
5
5. Write 76 = 117649 into logarithmic form.
6. Graph 𝑦 = 5(7)𝑥−1 + 3
y
12
10
8
6
4
2
x
-12
-10
-8
-6
-4
-2
2
-2
-4
-6
-8
-10
-12
4
7. Write the equation log128 16 = 7 in exponential form.
8. Condense to a single logarithm 2 log 3 2𝑥 + 5 log 3 𝑦
4
6
8
10
12
9. Graph 𝑦 = log 3 𝑥 − 2
y
12
10
8
6
4
2
x
-12
-10
-8
-6
-4
-2
2
4
6
8
10
12
-2
-4
-6
-8
-10
-12
10. Write as a single logarithm. 3 log 𝑟 − 5 log(𝑟 − 3)
3
11. Expand
log 𝑎 √
7𝑥
5
12. A company with loud machinery needs to cut its sound intensity to 47% of its original level. By how many decibels
would the loudness be reduced? Use the formula
. Round to the nearest hundredth.
13. Use the properties of logarithms to evaluate log 4 24 + log 4 128 − log 4 3
14. Solve 37𝑥 = 8288. Round to the nearest hundredth.
15. Solve log 2𝑥 + log 8 = 0. Round to the nearest hundredth if necessary.
16a. Simplify log 10−7
16b. Simplify ln 𝑒 7.5
17. A new truck costs $37,500 and depreciates at a rate of 11% each year. How much is the truck worth in 5 years?
18. In 2004 you invested $1250 which was compounded annually. In 2013 that investment is worth $1319.
Find the interest rate to the nearest tenth.
19. Without graphing, determine whether the function 𝑦 = (0.92)𝑥 represents exponential growth or exponential decay.
Explain your answer.
20. The parent function for the graph is of the form
.
y
20
a. Write the parent function.
18
16
14
12
b. Write a function for the translation left 3 units and
down 7 units.
10
8
6
4
2
x
-8
-6
-4
-2
2
21. Graph y = log (x + 1) + 4.
y
8
6
4
2
x
-8
-6
-4
-2
2
-2
-4
-6
-8
22. Solve 102x = 9. Show all work and round to the nearest hundredth.
4
6
8
4
6
8
23. $2350 is invested at a rate of 1.65% compounded quarterly. How much is the investment worth after 8 years? Show
all work.
24. $2350 is invested at a rate of 1.65% compounded continuously. How much is the investment worth after 8 years?
Show all work.
25. In a particular region of a national park, there are currently 380 deer, and the population is increasing at an annual rate
of 13%.
a. Write an exponential function to model the deer population.
b. Predict the number of deer that will be in the region after five years. Show your work.
c. If you can only begin to hunt in this area when the deer population reaches 1500, how long will it take until
you can hunt in this area?
26. The formula
gives the average atmospheric pressure P in pounds per square inch, at an altitude x in
miles above sea level. Find the elevation at which the average atmospheric pressure is 10.3 lb/in.2. Show the steps you
used to solve this problem.