Exam 3 Practice Problems Math 115: Precalculus July 28, 2009
Exam #3 will be on Thursday July 30, 2009 at 1:00pm and will cover sections 4.1,
4.2, 4.3, 4.4, 5.1, 5.2, 5.3, 5.4, 5.5, and 5.6 in Dugopolski’s Precalculus textbook. In
addition to the problems on this handout, you should review all quizzes, worksheets, and
homework assignments since exam 2.
1. Sketch a graph of each of the following functions. Identify the domain, range, and
whether it is increasing or decreasing.
(a) f(x)=4x(b) f(x) = 1
2x+2
−1 (c) f(x) = −5x−3+ 2
(d) f(x) = log(x) (e) f(x) = ln(x−2) + 3 (f) f(x) = −log(x+ 2) −4
2. Compute each logarithm without using a calculator.
(a) log41
16(b) ln(e3) (c) log2(32)
3. Solve each of the following exponential and logarithmic equations.
(a) 3x+2 =1
9(b) 4x+3 =1
2x(c) ex−2= 9
(d) log2(x) + log2(x−4) = log2(x+ 24) (e) log(x) + log(2x) = 5 (f) 2x−1= 33x
4. Fully expand the following logarithmic expressions. Your final answer should not
have any exponents or radicals inside the logarithms.
(a) ln rx
4(b) ln 3
√xy
t4/3(c) log43x√y
3
√x−1
5. Fully contract the following logarithmic expressions.
(a) ln(2) + ln(3) + ln(5) −ln(7) (b) 5 log 7(x)−4 log7(x2)
(c) log(2) + 2 log(x+y)−
2
3log(u−w)
6. Melinda invests her $80,000 winnings from Publishers Clearing House at a 9% annual
percentage rate. Find the amount of the investment at the end of 20 years if the interest
is compounded
(a) annually (b) quarterly (c) continuously
7. What amount must be deposited today in a certificate of deposit so that the in-
vestment will grow to $20,000 in 18 years at 6% compounded continuously?
8. Michael invests $800 at 3% compounded monthly. How long will it take for his
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