Name:
Date:
Algebra 2
Review for Test on Exponents, Logs, and Exponential Functions
You will be responsible for the following topics:






Exponent properties
Negative exponents
Fraction exponents
Solving equations with exponents and logarithms
Exponential modeling (word problems):
o Given a % rate of increase or decrease, find and use an exponential
function
o Given an input-output pair and a multiplier, find the starting value
o Given an exponential function, find the % rate of increase or decrease
o Given a starting amount and another point, find the exponential function
and the % rate of increase or decrease
o Given a starting value, multiplier, and output, find the exponent
Determine if a table/situation should be modeled with a linear or exponential
function
Review Problems:
Part I: Solve the following. Do not use your calculator for Part I.
1. log2 x = 4
2. 3log x 8 = 9
4. 32 x =
1
9
5. 5x 2 =125
3
3. x 4 = 8
6. log2 8- 3x =12
Name:
Date:
7. log17 1- x =11
8. 43x = 8x+2
Algebra 2
2
3
9. 5x =
1
5
10. 2log x 64 = 4
Part II: Use your calculator to complete Part II
1. Marta has a savings account that pays 1.5% interest annually. She has not made any
deposits or withdrawals for many years. Suppose that her current balance is
$4,516.32.
a. Write a function formula f(x) showing the amount of money in Marta’s account
after x years.
b. How much money was in her account 5 years ago? Show how you get your
answer.
Name:
Date:
Algebra 2
2. Of all the users of the web service Twitter, Katy Perry has the most followers. At the
start of year 2011, she had 7.5 million followers. Her number of followers has been
steadily increasing by 8% each month.
a. Let f(x) stand for how many followers Katy Perry has, x months after the start of year
2011.
Write a function formula for f(x).
b. How many followers did Katy Perry have at the start of 2013?
c. Solve graphically using the 2nd trace-intersect function on your calculator or by
algebra using logarithms. Round your answer to two decimal places. When did
the number of followers of Katy Perry surpass 15,000,000 ?
d. Solve by algebra using logarithms. Round your answer to two decimal places Solve
the equation f(x) = 30,000,000. Explain the meaning of the answer as it relates to
Katy Perry on Twitter.
Name:
Date:
Algebra 2
3. Giovanna has a bank certificate that pays 2.25% interest monthly. (Increases by
2.25% each month) She does not make any additional deposits or withdrawals. Her
current balance is $6,543.21.
a. How much was this certificate worth 2 years ago?
b. How much will the certificate be worth, 10 months from now?
4. Mrs. Chang owns a painting whose value has been growing exponentially. In the 6
years she’s owned the painting, its value has grown from $20,000 to $30,000.
a. By about what percent did the painting’s value grow each year?
b. Mrs. Chang will sell the painting when its value reaches $50,000. How long until
that happens? Solve algebraically using logarithms.
5. Mrs. Jones owns a painting whose value has been decreasing exponentially. In the 12
years she’s owned the painting, its value has decreases from $40,000 to $10,000.
a. By about what percent did the painting’s value decrease each year?
b. Let f(x) stand for the value of the painting, after x years. Write a function formula
for f(x).
c. When was the painting worth $5,000?
Name:
Date:
Algebra 2
6.
a. Jonah has been saving up to by a car that costs $3,000. So far he has saved $435.
Jonah just got a job at Mario’s, and he plans to save all of the money he earns to put
towards the car. He will make $10.25 per hour. How many hours will he have to
work before he can buy the car?
b. Jonah decides to invest the $435 in a savings account with a 3.15% interest rate
each month. If he does not withdraw or deposit any money, how much will be in the
account in 1 year?
7. Mr. Patrick owns a classic car whose value has been increasing by 3.5% each year.
The car is worth $5000. He wants to sell the car when it is worth $10,000. How many
years must he wait?
Name:
Date:
Algebra 2
Answers:
Part I:
1. x = 16
1
2. x = 2
3. x = 16
4. x = -
5. x = 5
2
6. x = -3
7. x = -11
8. x =
9. x = 1/125
10. x = 8
Part II:
1. a. f (x) = 4, 516.32(1.015)x
b. 4516.32 · (1.015)–5 = 4192.32, so the balance 5 years ago was $4,192.32.
2. a. f ( x ) = 7.5(1.08)x
b. f(24) ≈ 47.6 million followers
c. The graphs of Y1=7.5 · 1.08x and Y2= 15 intersect at x ≈ 9.006, so it took
about 9 months from the start of the year, meaning that it happened in late
September 2011.
d. x ≈ 18.01 so it took about 18 months from the start of 2011, so around June of
2012, for Katy Perry to have 30,000,000 followers.
3. a. f (- 24) = 6543.21(1.0225)
-24
= 3835.94
b. f (10) = 6543.21(1.0225) = 8173.80
10
4. a.
30,000 = 20,000b 6
3
= b6
2
æ3ö
b=ç ÷
è2ø
1/ 6
= 1.06991
So, the value of the painting grew by 6.99% per year.
b. x  13.56 years
Name:
Date:
Algebra 2
5. a.
10,000 = 40,000b12
1
= b12
4
æ1ö
b=ç ÷
è4ø
1 / 12
= .8909
So the painting’s value decreased by about 10.91% per year
b. f (x) = 40, 000(.8909)x
c. x  18 years
6. a. 10.25x + 435 = 3, 000
x  250.24 or about 251 hours
b. 435(1.0315)12 = $631.13
7. Y1= 5,000(1.035)
x
Y2=10,000
x=20.15 years