Answer to worksheet 3.3 and 3.4
1. The value of a painting is increasing exponentially and satisfies the differential
equation where t is measured in years and
P
(
t
) is the value of the painting in millions of
dollars.
Use the differential equation
to determine how fast the value will be increasing
when the value reaches $5 million. Write your answer in a sentence, and use appropriate
units.
P
′
(
t
)
=
.08(5)
=
.4 When the painting’s value reaches $5 million, the value will be
increasing at a rate of $.4million ($400,000) per year.
2. The United States federal budget submitted by President Clinton for 2000 was $1.8
trillion. The United States federal budget submitted by President Bush for 2005 was $2.4
trillion. Assume that the United States federal budget grows at a rate proportional to its
size and let the year 2000 correspond to t = 0.
(a)
Find the growth constant k
correct to four decimal places
for this situation.
P
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 Fall '10
 LindaAbel
 Exponential Function, Radioactive Decay, States Federal Budget

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