Project 21
MAC 2311
1. Suppose the value (in dollars) of some electronic equipment
t
years from now is given by
V
(
t
) = 1000

400 ln(1 +
t
2
)
.
Find the value of the equipment
1
year from now. (Round to the nearest dollar.)
Find 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
2
years from now. (Don’t plug in 2!!—
guess!)
You just used differentials and linearization. Let’s show it. . . Start by calculating the formula
for the differential
dV
. What quantity does it approximate?
To approximate the change in cost from year
1
to year
2
, what would be the values of
t
and
dt
that you should put into the differential
dV
? Evaluate the differential with these values.
Find the linearization
L
of
V
(
t
)
at
t
= 1
, and use it to approximate
V
(2)
, the value of the
electronic equipment
2
years from now. Was this your original guess?. Show that, in general,
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 Spring '08
 ALL
 Calculus, diﬀerential dV

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