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
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This note was uploaded on 12/27/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.
- Spring '08
- Smith
- Calculus
-
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