Pre-Calculus
Unit 10 Exam:
Name ___________________________
“Exponential and Logarithmic Functions” (Practice Exam)
(10-1) Sketch each exponential function by hand.
#1
𝑦 = 2𝑥
#2
𝑓(𝑥 ) = 4−𝑥
#3
The function below 𝑦1 = 𝑒 𝑥 . Give an
expression for 𝑦2 below.
#4.
An investment of $11,000 earns interest
(10-2) compounded continuously at a rate of 8%.
What will its value be after 20 years?
#5.
A known radioactive isotope has a half-life
of 1288 years. A certain sample of the
isotope can be modeled by
1 𝑡/1288
𝑦 = 60 ( )
, where y is the amount of
2
the isotope present (in grams) after t years.
(a)
What is the initial mass of the
sample?
(b)
How much of the sample will be left
after 3000 years?
#6.
Evaluate each expression.
(10-3)
(a)
log 3 243
1
(b)
log 5 25
(c)
ln(𝑒 8 )
(d)
log 6 1
(10-4) Sketch each function by hand.
#7.
𝑓(𝑥 ) = log 2 𝑥
#8.
𝑔(𝑥 ) = − log 4 𝑥
(10-5) Evaluate.
#9
log 4 10
#10.
log 2.7 1.82
Expand each expression.
#11.
ln(𝑒𝑥 2 )
#12.
log 𝑎 (𝑧 )
1
Condense each expression.
#13.
#14.
1
2
ln 𝑎 + ln 𝑏 − 3 ln 𝑐
2(log 𝑛 𝑝 + log 𝑛 𝑞) − log 𝑛 (𝑥 − 5)
(10-6) Solve each equation.
1
#15.
5𝑥 =
#16.
𝑒 3𝑥 = 11
#17.
6 ⋅ 2𝑥 + 4 = 37
625
(10-7) Solve each equation.
#18.
log 10 𝑥 = 3.6
#19.
− ln(𝑒𝑥 ) + 3 = −9
#20.
log 𝑎 𝑥 + log 𝑎 (𝑥 − 4) = log 𝑎 5
#21. Given the population data below for bacteria
(10-8) in a petri dish:
Time (hrs.)
0
2
3
5
6
8
11
Population
30
61
88
151
179
355
768
(a)
Find a best-fitting exponential model
of the form 𝑦 = 𝑎 ⋅ 𝑏𝑥 , where y is
the population in the dish after x
hours.
(b)
Use the model from (a) to predict the
population of the dish after 24 hours.
#22. Given the data below:
(10-9)
x
0.5
1
2
5
8
10
17
y
-3
1
1.4
3
3.9
4.4
5.3
(a)
Find a best-fitting logarithmic model
of the form 𝑦 = 𝑎 + 𝑏 ⋅ ln 𝑥 for the
data.
(b)
Use the model from (a) to predict the
value of x when y = 8.