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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

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

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

**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

That is,

The rate of change of the ripple at time *t* is,

Therefore, the rate at which the rate of change of the area within the circle is increasing after 1 s is,

(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

The rate at which the rate of change of the area within the circle is increasing after 3 s is,

From part (a), the rate of change of the ripple at time *t* is,

Therefore, the rate at which the rate of change of the area within the circle is increasing after 3 s is,

(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

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

From part (a), the rate of change of the ripple at time *t* is,

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

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