Math 1314
Test 3 Review
Material covered is from Lessons 9 – 15
Math 1314 Test 3 Review 1
Math 1314
Test 3 Review
Material covered is from Lessons 9 – 15
1. The total weekly cost of manufacturing x cameras is given by the cost function:
= −.03
+ 80 + 3000 and the revenue function is
= −.02
+ 600.
Use the marginal profit function to approximate the actual profit realized on the sale of the
234
th
unit.
2. A music company produces a variety of electric guitars. The total cost of producing x
guitars
is given by the function
2
1
( ) 6100 7
5
C x x x
= + −
where C(x) is given in dollars. Find the average
cost of producing 130 guitars.
Recall:
( )
( )
C x
C x
x
=
Recall:
Demand is said to be elastic if
( ) 1
E p
>
.
Demand is said to be unitary if
( ) 1
E p
=
.
Demand is said to be inelastic if
( ) 1
E p
<
.
3. Suppose E(p) =
1
⁄
4
when the price of the item is p. Then the demand is
a. Elastic b. Unitary c. Inelastic
4. Suppose the demand equation of a product is given by p = -0.04x + 1000 where the function
gives the unit price in dollars when x
units are demanded. Compute E(p) when
p = 535 and interpret the results.
Recall:
( )
( )
( )
p f p
E p
f p
′
⋅
= −
Math 1314 Test 3 Review 2
5. The sales from company ABC for the years 1998 - 2003 are given below.
Year 1998
1999
2000
2001
2002
2003
Profits in millions of dollars
36.3 39.1 41.7 44.6 47.9 49.9
Rescale the data so that x = 0 corresponds to 1998.
A. Find an exponential regression model.
Command: Answer:
B. Find the rate at which the company's sales were changing in 2007.
Command: Answer:
6. The number of deer present in a nature preserve can be expressed using the model
0.6
125
( )
1 31
t
N t
e
−
=
+
, where N(t) gives the number of deer and t
gives the number of months since
the initial count of deer was taken. Enter the function in GGB.
A. How many deer will be present after 6 months?
Command: Answer:
B. At what rate is the population changing after 6 months?
Command: Answer:
Math 1314 Test 3 Review 3
7. . At the beginning of an experiment, a researcher has 511 grams of a substance. If the half-
life of the substance is 16 days:
A. Identify two points given in the problem.
B. Find an exponential regression model using the two points in part a.
Command: Answer:
C. How many grams of the substance are left after 25 days?
Command: Answer:
D. What is the rate of change after 10 days?
Command: Answer:
8. The graph given below is the first derivative of a function, f.
A. Find any critical numbers of f. B. Find any intervals where the f is
increasing/decreasing.
