BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.8, Problem 14E

(a)

To determine

To find: The rate at which the rate of change of the area within the circle is increasing after 1 s.

Expert Solution

Answer to Problem 14E

The rate at which the rate of change of the area within the circle is increasing after 1 s is, 7200πcm2/s.

Explanation of Solution

Given:

A stone which is dropped into a lake that creates a circular ripple whose speed when it travels outward is 60 cm/s.

Calculation:

Area inside the ripple at time t is A(t)=π(60t)2.

That is, A(t)=3600πt2.

The rate of change of the ripple at time t is, A'(t)=7200πt.

Therefore, the rate at which the rate of change of the area within the circle is increasing after 1 s is, A(1)=7200πcm2/s.

(b)

To determine

To find: The rate at which the rate of change of the area within the circle is increasing after 3 s.

Expert Solution

Answer to Problem 14E

The rate at which the rate of change of the area within the circle is increasing after 3 s is, 21,600πcm2/s.

Explanation of Solution

From part (a), the rate of change of the ripple at time t is, A'(t)=7200πt.

Therefore, the rate at which the rate of change of the area within the circle is increasing after 3 s is, A(3)=21,600πcm2/s.

(c)

To determine

To find: The rate at which the rate of change of the area within the circle is increasing after 5 s. What can be concluded from the parts (a), (b) and (c).

Expert Solution

Answer to Problem 14E

The rate at which the rate of change of the area within the circle is increasing after 5 s is, 36000πcm2/s.

Explanation of Solution

From part (a), the rate of change of the ripple at time t is, A'(t)=7200πt.

Therefore, the rate at which the rate of change of the area within the circle is increasing after 5 s is, 36000πcm2/s.

From the parts (a), (b) and (c), it can be concluded that the rate of change increases as time increases.

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