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.
This
preview
has intentionally blurred sections.
Sign up to view the full version.
This is the end of the preview.
Sign up
to
access the rest of the document.
- Spring '08
- Smith
- Calculus, 2 years, $800, 1 1 years, 1 4 years
-
Click to edit the document details
