Section 5.4 (cont.)
3) The rate of change of the length of the average hospital stay between 1980 and 1996 can be
modeled by the equation
where
t
is the number of years
s t
t
days per year when
t
t
days per year when
t
( )
.
.
.
.
=
−
≤
<
−
+
≤
≤
0028
023
0
10
00408
030833
10
16
since 1980.
Determine the values of the following definite integrals and interpret your answers.
a)
s t dt
( )
0
10
∫
b)
s t dt
( )
10
16
∫
c)
s t dt
( )
0
16
∫
4) Many businesses spend money each year on advertising in order to stimulate sales of their
products. The data given in the table show the approximate increase in sales (in thousands of
dollars) that an additional $100 spent on advertising, at various levels, can be expected to
generate.
a) Find a model for these data.
b) Use the model in part
a
to
determine a model for the total
sales revenue as a function of the
amount
x
spent on advertising.
Use the fact that revenue is 500
thousand dollars when $1000 is
spent on advertising.
c) Find the point where returns
begin to diminish for sales
revenue.
d) The managers of the business
are considering an increase in
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 Fall '08
 Royer
 Calculus, Derivative, Rate Of Change, 1912, average hospital stay

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