Worksheet 6.1 - Integral As Net Change - Calculus Maximus Page 4
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9Calculus Maximus
WS 6.1: Integral as Net Change
7. The rate at which people enter an amusement park on a given day is modeled by the function E defined
by
15600
E t
.
2
t
24
t
160
The rate at which people leave the same amusement park on the same day is modeled by the function L
defined by
9890
L t
.
2
t
38
t
370
Both
E t and
L t are measured in people per hour, and time t is measured in hours after midnight.
t
t , there
These functions are valid for
9, 23
, which are the hours that the park is open. At time
9
are no people in the park.
t
(a) How many people have entered the park by 5:00 P.M. (
17
)? Round your answer to the nearest
whole number.
(b) The price of admission to the park is $15 until 5:00 P.M.. After 5:00 P.M., the price of admission to
the park is $11. How many dollars are collected from admissions to the park on the given day?
t
t
(c) Let
H t
E x
L x dx
for
9, 23
. The value of
H
17
to the nearest whole number is
9
H
H
3725. Find the value of
17
and explain the meaning of
H
17
and
17
in the context of
the park.
t
(d) At what time t, for
9, 23
, does the model predict that the number of people in the park is a
maximum?
Page 4 of 9
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