Name:
College Algebra – Chapter 4 Part 2 Review Problems
Period:
Complete 15 of the following problems.
Solve for x.



1. log 7 x  5x  log 7 x  5x  30
2
2

2. log 5 ( x  4 x  4)  2
2
3. log 6 (2 x  6 x  40)  2
4. log 4 ( x  9)  log 4 ( x  3)  3
5. log 5 x  log 5 ( x  4)  2
6. 2 log 3 ( x )  log 3 (2x  5)  2
7. log 9 x  3 log 3 x  14
8. log 8 ( x )  5 log 2 x  16
2
2
9. log 4 ( x 1)  log 4 ( x  6)  log 4 ( x  2)  log 4 ( x  3)
1 2 x
10. 4
13. 2
3x
2
 32x 1
11. 25
2x
 5x
2 12
14. 16  3  4
x
x 1
 35  0
12. 3
15. 5
x 2
5
x 2
 7 x2
16. In 1970, Joe invested $2,000 into a savings account.
(a) If the investment grows at 6% compounded monthly, how much is it worth now in 2012?
Round to the nearest dollar. Use the formula and verify using the Finance APP.
b) After how many years will the investment be worth $20,000? Round to one decimal place. Use the formula
and verify using the Finance APP.
c) How long would it take for the investment to quadruple if it is compounded continuously?
Round to one decimal place. Use the formula and verify using the Finance APP.
d) How much would Joe have had to invest back in 1970 for his investment to be worth $25,000 now, in 2012
assuming 6% compounded monthly? Round to the nearest dollar. Use the formula and verify using the
Finance APP.
17. How long does it take for an investment to double if you earn 10% compounded continuously? Use the
formula and verify using the Finance APP.
18. How long does it take for an investment to triple if it is compounded quarterly at 12%? Use the formula
and verify using the Finance APP.
19. If your parents started a college fund when you turned 5 years old with $5,000 and it has earned 12% per
year, compounded monthly since your 5th birthday. How old would you be when the college account is
worth $25,000? Use the formula and verify using the Finance APP.
20. What is the effective interest rate for an investment earning 8% compounded monthly? Use the formula
and verify using the Finance APP.
21. What rate of interest is required to quadruple an investment in 5 years if it is compounded quarterly? Use
the formula and verify using the Finance APP.
For 22 - 24, assume increases can be modeled according to uninhibited exponential growth/decay.
22. If the cost of attending Stanford for a year was $10,000 in 1980 and this cost had risen to $21,500 in 1990,
what would the cost be in 2010?
23. Assume the government mandates that the fuel economy of all trucks must increase by a required amount
each year. If the average fuel economy of a HUMMER in 2000 was 13 mpg city and in 2005 the mpg had risen
to 14.4, how many years will it take before the HUMMER gets over 25 mpg city? Round to one decimal place.
24. The population of a certain town was 2500 at the start of 1993 and had risen to 3520 at the start of the
year 2000. During what year will the population of the town reach 5000 people?
25. A skillet is removed from an oven whose temperature is 4750F and placed in a room whose temperature is
70F. After 5 minutes, the temperature of the skillet has cooled to 4250F. How long will it be until the skillet’s
temperature is 1500F?
26. Sandy manages a ceramics shop and uses a 6500F kiln to fire her ceramic green ware. After turning off
her kiln she must wait until its temperature gauge reaches 1600F before opening it and removing the ceramic
pieces. If room temperature is 800F and the gauge reads 6000F in 12 minutes, how long must she wait before
opening the kiln?
27. Jen backs out of her garage at noon on a nice spring day to run an errand. Unfortunately, she accidentally
runs over a rabbit in her driveway on her way out of the garage. She doesn’t realize that she ran over the rabbit
and she continues on her way. If the rabbit’s temperature has cooled to 960F at 1PM and it is measured to be
850F when she returns from her errand, what time did she get back from her errand? Assume a healthy rabbit
has a body temperature of 1010F and the outside temperature can be considered to be a constant 600F.
28. A cup of coffee is heated to 1940F is then allowed to cool in a room whose air temperature is 720F. After
11 minutes the temperature of the cup of coffee is 1400F. Find the time needed for the coffee to cool to a
temperature of 1020F.