Accumulation
Authors: Bill Davis, Horacio Porta and Jerry Uhl
©19962007
Publisher: Math Everywhere, Inc.
Version 6.0
2.03 Measurements
LITERACY
What you should be able to handle away from the machine.
·
L.1)
When you are fresh, you find that you can harvest 150 bushels of corn per hour. But as the
day wears on, your efficiency is somewhat decreased. In fact, after t hours from the
beginning of the day, you find that you are harvesting at a rate of
150 e

0.5t
bushels per hour.
Write down the integral that measures how many bushels of corn you harvest after arriving
in the field fresh as a daisy and working for 5 consecutive hours.
·
L.2)
At this moment, you borrow $10, 000 at an interest rate of 7
%
per year compounded every
instant. Assuming you borrow no new money and that you pay off none of the loan for the
next three years, write down the integral that measures what you owe three years from now.
·
L.3)
You have a profitmaking scheme that is projected to pay profits at a rate ot
p
@
t
D
=
100000 e

2t
dollars per year t years from now. Assuming a projected interest rate of 6
%
per year
compounded every instant, what is the present value of your scheme?
·
L.4)
The base of a certain solid is the circle x
2
+
y
2
=
4 in the xyplane.
Each cross section cut by a plane perpendicular to the xaxis is a square.
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 Spring '08
 Kim
 Math, td

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