MAC3233 Test 4 August 9, 1995
Name
Instructions:
This is a
closedbook, closednotes
test. Do
not
write your answers on this paper,
use separate answer sheets.
No calculators
are allowed to be used. To receive credit, you must
show all
work
.
Some numerical answers may involve the function ln or the number
e
.
1. (5 points) Let
P
(
t
) be the number of bacteria present in a culture after
t
minutes, and suppose that
P
(
t
) satisﬁes the diﬀerential equation
P
0
(
t
) = 0
.
35
P
(
t
)
.
Find the formula for
P
(
t
) if initially there are approximately 13,500 bacteria present.
2. (15 points) Suppose that the velocity of a model car at time
t
is
1
t
+
t
inches per second where
t
is in
seconds and 1
≤
t
≤
10.
(a) Find the area under the graph of the velocity curve from
t
= 1 to
t
= 10.
(b) What does the area in part (a) represent?
3. (15 points) A company can sell
q
=
400
50 +
p
2
refrigerators at a price of
p
hundred dollars per refrigerator.
(a) Find
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