Chapter 10.5, Problem 37E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Revenue** A recently released film has its weekly revenue given by

*R(t)* is in millions of dollars and *t* is in weeks.

(a) Graph *R(t).*

(b) When will revenue be maximized?

(c) Suppose that if revenue decreases for 4 consecutive weeks, the film will be removed from theaters and will be released as a video 12 weeks later. When will the video come out?

**(a)**

To determine

**To graph:** The revenue function

Explanation

**Given Information:**

The provided function *t* is the time in weeks and

**Graph:**

Consider the provided function,

First calculate the rate of change of *t.*

Thus, differentiate the function with respect to *t.*

Use the quotient rule to differentiate the function,

Calculate further,

The maximum exists at the critical value where

Thus, for critical value

Solve further,

Find

Which is

Therefore, the revenue starts decreasing after

**(b)**

To determine

**To calculate:** The value of *t* at which *t* is the time in weeks and

**(c)**

To determine

**To calculate:** The value of *t* at which the movie released as a video if it was to supposed to be removed from cinema after revenue decreases for 4 weeks and was supposed to be released as a video after 12 weeks of getting removed from cinema.

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