Project 17/18
MAC 2233
1. The idea of a differential is pretty simple if you can get past the notation. Consider the fol
lowing problem: Suppose the value (in dollars) of some electronic equipment
t
years from
now is given by
V
(
t
) = 400 +
1600
1 +
t
2
.
Find the value of the equipment
1
year from now, and the rate at which the value of the
equipment is changing with respect to time
1
year from now. Include units (very important
for the next question).
1200
dollars; 
$
800
per year
Based only on common sense and your answers to the previous two questions, explain what
you would guess to be the value of the equipment
1
1
4
years from now. (Don’t plug in. . . guess!)
1000
dollars
You just used differentials. Let’s show it. . . Start by calculating the formula for the differential
dV
. What quantity does it approximate?
d
V
=

3200
t
(1 +
t
2
)
2
d
t
per year
To approximate the change in value
V
from year
1
to year
1
1
4
, what would be the values of
t
and
dt
that you should put into the differential
dV
?
Evaluate the differential with these
values.
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 Spring '08
 Smith
 Calculus, 2 years, $800, 1 1 years, 1 4 years

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