M119 Chapter 4 Review
1. a) Write in
logarithmic form: 
b)
Write in exponential form: 
2.
Evaluate without a calculator:
a)
b) 
3. For
the function 
, use calculus to determine
a)
intervals of increase and decrease b) relative extrema
4.
Solve for x:
a) 
b) 
c) 
5. Find
the derivative: 
6. Find
the derivative: 
7. Find
the derivative: 
9. Find
the derivative: 
10. Find the derivative: 
11. Find the derivative: 
12. Find the derivative: 
13. Determine where the given function is
increasing and decreasing.
Find the relative extrema and sketch
the graph:
a) 
b) 
14. If $4,500 is invested at an annual
rate of 8%, find the balance after 5 years
if the
interest is compounded:
a)
annually b) quarterly
c)
monthly d) continuously
e)
How long will it take for the money to triple if compounded
continuously?
15. A home loan is made for $200,000 at 6.75%
annual interest rate,
compounded
monthly, for 15 years. What is the
monthly mortgage payment
on this
loan? (use the
AMORT program or the formula on page 307)
16. Radium decays exponentially. Its half-life is 1,690 years. How long will it
take for a
200-gram sample of radium to be reduced to 150 grams.?
17. The daily output of a worker who has been on
the job for t weeks is
units. Initially the worker could produce 40 units
per day,
and after 8
weeks the worker could produce 80 units per day.
a)
Find the specific values of A
and k to find the specific Q(t) function.
b)
How many units could the worker produce a day after 12 weeks?
18. A certain industrial machine depreciates so
that its value after t years is
dollars.
a)
At what rate is the value of the machine changing with respect to time
after 5
years?
b)
At what percentage rate is the value of the machine changing with
respect to
time after t years?
19. The aerobic rating of a person x years old is 
for 
.
Use calculus to determine at what age
aerobic capacity is maximized.
SOLUTIONS
1. a) ln 20.09855 ~ 3 b) 
2. a) 
b)
3. a) 
b)
Relative Maximum is 32.82 at x
= 4; Relative minimum is 0
at x = 0
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. “Log Law:
12. 
13. 
14. 
15. Using AMORT payment is $1769.82
16. Half-life implies 
How long until 150 grams 
17. Given:
18. 
19. 
