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).
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!)
You just used differentials. Let’s show it. . . Start by calculating the formula for the differential
dV
. What quantity does it approximate?
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, 4 inches, 1 1 years

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