Oregon Institute of Technology
Math 111 — Sample Exam 3
Name:
Directions: To receive full-credit, show work and circle or box answers. Problems are worth
6 points each unless otherwise stated.
1. (4 pts) Short answer questions about exponential and logarithmic functions.
(a) If f (x) = Ax , then f −1 (x) =
.
(b) If f (x) = ln x, then f −1 (x) =
.
(c) State the domain and range of f (x) = log7 x.
Domain:
Range:
(d) State the domain and range of f (x) = 2x .
Domain:
2. Rewrite the expression 4 ln x −
4 ln x −
Range:
1
ln y + 3 ln z as a single logarithm.
2
1
ln y + 3 ln z = ln (
2
)
3. Solve the following equation for t. Show some work and round your answer to 2 places:
1000 = 100 (1.0025)5t + 300
1
4. The rat population in Ratsville USA (a major metropolitan city) is given by the formula
P (t) = 18e0.09t where t is measured in years since 2003 and P is measured in millions.
(a) What was the rat population in 2003?
(b) What is the rat population going to be in the year 2015 ?
5. (4 pts) Use the graph on the left to sketch a graph of y = f −1 (x) on the right.
Graph of y = f (x)
Graph of y = f −1 (x)
y
6
y
6
5
5
4
4
3
3
2
2
1
1
x
x
0
-6
-5
-4
-3
-2
-1
0
0
1
2
3
4
5
6
-6
-5
-4
-3
-2
-1
0
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
2
1
2
3
4
5
6
6. At the beginning of an experiment, a scientist has 250 grams of radioactive Watermanium. After 125 minutes, her sample has decayed to 90 grams. The model for
exponential decay is N(t) = N0 ekt .
Determine the values of N0 and k. Round k to 5 decimal places.
N0 =
grams
k≈
7. The intensity of a 8MHz ultrasound transducer at the point where it is applied to the
skin is 10µW/ cm2 (microwatts per square centimeter). The attenuation for such a
transducer is −4dB per centimeter of depth into soft tissue. What will the intensity
of the transducer be at a depth of 3cm? Inlcude units with your answer.
attenuation = 10 log10
I2
I1
where I1 is the intensity at skin surface.
8. Suppose 10 thousand dollars is invested in an account that earns 6% annual interest
compounded monthly. Approximately how many years will it take the investment to
grow to $16,000?
The model for compound interest is A(t) = P 1 +
show work.
3
r
n
nt
. Set up and solve an equation,
9. Use the equation to determine the radius and coordinates of the center of the circle :
(a) (x − 3)2 + (x + 5)2 = 100
Center:
Radius:
(b) (x + 4)2 + (x − 6)2 = 64
Center:
Radius:
(c) Complete the squares first: x2 − 6x + y 2 + y = 10
Center:
Radius:
4