College Algebra
Chapter 4 Part 2 Take Home Quiz
Due: Monday April 15th
Name
Directions: Show all work and reasoning to receive full credit.
12
 7 x3 5 1  4 x 
1) Expand the logarithm completely: ln 
 ( x  3)8 


.
2) Condense the logarithm by writing it as a single logarithm:
3) Solve the exponential equation for x: 3e x4  5  10 .
1
3log( x  1)  2 log( x  1)  3log 2 x .
5
4) Solve the logarithmic equation for x: ln(7  x)  ln(3x  5)  ln(24 x ) .


 
5) Solve the logarithmic equation for x: loga x2  7  2log a  2 x   log a 2 x2 .
6) Determine the amount of money that should be invested at a rate of 8% compounded quarterly to produce a
final balance of $20,000.00 in 10 years.
7) After discontinuing all advertising for a certain product in 1994, the manufacturer noted
that sales began to drop according to the given model. Where S represents the number of
units sold and t = 0 represents 1994. In 1996, the company sold 300,000 units.
a) Complete the model by solving for k.
S
500, 000
1  0.6ekt
b) Estimate sales in 2010.
8) An initial deposit of $4,500.00 is made in a savings account for which the interest is compounded
continuously. The balance of the account will triple in 12 years. When will the balance of the account reach
$35,000?
9) The half-life of a radioactive substance is 60 days. Find the amount of the substance remaining after 145
days, to the nearest thousandths, if the original amount of the sample is 25 grams.
10) Determine the annual rate of interest compounded continuously for the sum of money in an account to
become triple the original amount in 10 years.
11) Determine the effective rate of interest of an investment that is continuously compounded at a rate of
12.75%.
12) You baked chocolate chips cookies for your mom on Mother’s Day. The cookies came out of a 3250F oven
and you let them cool. After 15 minutes, the cookies are 3000F. If you must wait for the cookies to be 1250F
before you can serve them to your mom, how long does your mother have to wait before she can enjoy your
cookies? (Room temperature is 720F.)
Solve.
13) 25𝑥 − 5𝑥+1 − 4 = 0
15) 62𝑥 = 53𝑥−1
17) ln 6 − ln(5 − 𝑥) = ln⁡𝑥
14)
𝑒 𝑥 −32𝑒 −𝑥
4
=1
16) 3 log 3 𝑥 + log 9 𝑥 = 7