College Algebra
Chapter 4 Part 2 Test
Name
Directions: Show all work and reasoning to receive full credit.
Question 0 (1 point): What would you do with a million dollars?? _____________________________________
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1) Expand the logarithm completely: log 𝑏
4
√
𝑥 5𝑦7
𝑧2
1
2) Condense the logarithm by writing it as a single logarithm: log 2 (𝑥 2 − 9) + 3 log 2 (2𝑥 − 5) − 2 log 2 (𝑥 + 3)
(Completely simplify!)
3) Solve the exponential equation for x: 35𝑥−1 = 5
4) Solve the logarithmic equation for x: log 7 (𝑥 + 4) = log 7 (12 − 𝑥) − log 7 (𝑥 − 3)
5) An initial deposit of $4,100 is made in a savings account for which the interest is compounded continuously.
a) If the balance will double in seven
years, find the interest rate of the account.
b) When will the balance in the account reach
$20,000?
6) Assume the average selling price of a home in Fort Collins grows according to the exponential model 𝐴(𝑡) =
𝐴0 𝑒 𝑘𝑡 , where t is time in years. If the average selling price was $25,600 in 1976 and it was $226,400 in 2007
(31 years later), predict the average selling price of a home in Fort Collins in the year 2030.
7) Students in an algebra class were given an exam and then tested once a month with an equivalent exam. The
average score for the class was given by the human memory model equation 𝑓(𝑡) = 84 − 16 log(𝑡 + 1), where
t is time in months. How many months will it take for the class average to be 72?
8) The half-life of radioactive cobalt is 4.9 years. If a sample presently contains 120 grams of radioactive cobalt
now, how much will be present in 25 years?
9) Assume your parents invested $15,000 into a stock fund when you are born to be used for your college
education. The investment does well, on average, and the value grows 6% compounded monthly.
a) How much will the investment be worth on your 18th birthday?
b) How many years will it take for the bond to double in value?
c) How much would you have had to invest initially in order for the investment to be worth $50,000 on
your 18th birthday?
d) If instead the investment is compounded continuously at 6%, how many years will it take for the
investment to triple in value?
Solve.
10) 22𝑥 − 2𝑥+1 − 15 = 0
12) 53𝑥 = 43𝑥+1
14) ln 12 − ln(7 − 𝑥) = ln⁡𝑥
11) 2log 4 (𝑥 + 3) − log 4 25 = 2
13) 3 log 5 𝑥 + log 25 𝑥 = 14