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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after {a) 1 s, (b) 3 s, and (c) 5 s. What can you conclude?

(a)

To determine

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

Explanation

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

(b)

To determine

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

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