Algebra II
Name___________________________
Exponential and Logarithmic Functions Test
Study Guide
Carefully graph each function. You may use your calculator, but be sure to clearly mark
at least 3 points on each graph. You must provide a table!
1)
y = 5 ⋅ 2x
2)
⎛ 3 ⎞
y = 8 ⎜ ⎟
⎝ 4 ⎠
3)
y = log 2 x
4)
y = 3ln x
x
For problems 5 and 6, you will be given 2 points on a growth/decay function in the form
𝒚 = 𝒂𝒃𝒙 . Find the function.
5)
(0, 4), (2, 8)
6)
(0, 10), (3, 1.25)
Problems 7 through 9 are application problems from the unit. You will be writing a
function, then answering a question using the function you created.
7)
Rylie scored 14 goals last season. Because she gets to play against Bloomsburg so often,
it is expected that her scoring will increase by 3% per year. First, write an exponential
function in the form 𝑦 = 𝑎𝑏 ! to model Rylie’s scoring. Then use your function to
determine how many points she will score in 5 years. Round your answer to the
nearest point.
8)
You just purchased a new laptop computer for $700. It depreciates in value by 20% per
year. First, create an exponential function in the form 𝑦 = 𝑎𝑏 ! to model the value of the
laptop. Then use your function to determine how long it will take for the value of the
computer to decrease to $300. Round your answer to the nearest tenth of a year.
9)
The radioactive element Maiahdon has a half-life of 500 years. You have a 40 gram
sample of this element. First, write an exponential function to model this situation. Then
use your function to determine how much Miahdon is remaining after 800 years. Round
your answer to the nearest tenth of a gram.
Write each exponential equation in logarithmic form.
10)
73 = 343
11)
10−2 = 0.01
Write each logarithmic equation in exponential form.
12)
log5 25 = 2
13)
ln1 = 0
Use the properties of logarithms we learned to write each expression as a single logarithm.
14)
log 4 x + log 4 y − log 4 z
15)
1
3log m + log w
2
Use the properties of logarithms we learned to expand each logarithm as far as possible.
16)
log9
ab
c
17)
ln ( xy 7 )
Solve each equation. Give an exact answer and a decimal approximation accurate to three
places.
18)
6 x = 79
19)
42 x +3 = 7
20)
log 7 x = 4
21)
4 log ( x − 3) = 8
Solve each equation. Give an exact answer and a decimal approximation accurate to three
places.
22)
e x = 400
23)
7e 2 x − 4 = 17
24)
ln x = −3
25)
⎛ 2 x ⎞
−5 + ln ⎜ ⎟ = 6
⎝ 3 ⎠
One more word problem…. Using the formula for compound interest, A=Pert, assuming you
put $500 into an account earning 13% interest compounded continuously, how long will it take
for you to have $2000 in your account?