Unit 10 Practice Exam

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Pre-Calculus
Unit 10 Exam:
Name ___________________________
β€œExponential and Logarithmic Functions” (Practice Exam)
(10-1) Sketch each exponential function by hand.
#1
𝑦 = 2π‘₯
#2
𝑓(π‘₯ ) = 4βˆ’π‘₯
#3
The function below 𝑦1 = 𝑒 π‘₯ . 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 𝑑/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(π‘₯ ) = log 2 π‘₯
#8.
𝑔(π‘₯ ) = βˆ’ log 4 π‘₯
(10-5) Evaluate.
#9
log 4 10
#10.
log 2.7 1.82
Expand each expression.
#11.
ln(𝑒π‘₯ 2 )
#12.
log π‘Ž (𝑧 )
1
Condense each expression.
#13.
#14.
1
2
ln π‘Ž + ln 𝑏 βˆ’ 3 ln 𝑐
2(log 𝑛 𝑝 + log 𝑛 π‘ž) βˆ’ log 𝑛 (π‘₯ βˆ’ 5)
(10-6) Solve each equation.
1
#15.
5π‘₯ =
#16.
𝑒 3π‘₯ = 11
#17.
6 β‹… 2π‘₯ + 4 = 37
625
(10-7) Solve each equation.
#18.
log 10 π‘₯ = 3.6
#19.
βˆ’ ln(𝑒π‘₯ ) + 3 = βˆ’9
#20.
log π‘Ž π‘₯ + log π‘Ž (π‘₯ βˆ’ 4) = log π‘Ž 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 = π‘Ž β‹… 𝑏π‘₯ , 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 = π‘Ž + 𝑏 β‹… ln π‘₯ for the
data.
(b)
Use the model from (a) to predict the
value of x when y = 8.
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