Sophie L.

asked • 10/19/20

Is there a time t , for 1<t<8 , at which the rate of change of the number of people at the venue changes from negative to positive? Give a reason for your answer.

"For time 0 ≤ t ≤ 8, people arrive at a venue for an outdoor concert at a rate modeled by the function A defined by A(t) = 0.3sin(1.9t) + 0.3cos(0.6t) + 1.3. For time 0 ≤ t ≤ 1, no one leaves the venue, and for time 1 ≤ t ≤ 8, people leave the venue at a rate modeled by the function L defined by L(t) = 0.2cos(1.9t) + 0.2sin (t) + 0.8. Both A(t) and L(t) are measured in hundreds of people per hour, and t is measured in hours. The number of people at the venue, in hundreds, at time t hours is given by P(t)."

Paul M.

tutor
The only sensible way to answer this question is with graph...try DESMOS or your graphing calculator,
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10/19/20

1 Expert Answer

By:

Jeffrey K.

This solution seems to ignore the condition that L(t) = 0 for 0 <= t <= 1. If it is taken into account, P(t) will be slightly larger for 0 <= t <= 8.
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10/19/20

Sa M.

P(t) is the amount of people, so P'(t) = A(t) - L(t)
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03/17/21

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