a. Explanation Given: The amount of water (in gallons) left in a bucket which is leaking is given by: Q ( t ) = 5 ( 1 − t 25 ) 2 ......(1) Formula used: d d x ( a f ( x ) ) = a [ d d x ( f ( x ) ) ] , d d x ( x n ) = n x n − 1 Calculations: The rate of change of Q ( t ) with respect to time is given by, Q ′ ( t ) = d d t [ 5 ( 1 − t 25 ) 2 ] = 5 d d t [ ( 1 − t 25 ) b. To determine To find: the time it takesfor all the water to leak out of the bucket. c. To determine To find: the rate of water leakage when last drop leaks out.

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Differential Equations

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Chapter 3.4, Problem 38PS

To determine

To find:the rate (to the nearest hundredth gallons) at which water is leaking after 2 seconds.

To determine

To find: the time it takesfor all the water to leak out of the bucket.

To determine

To find: the rate of water leakage when last drop leaks out.

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Chapter 3.4, Problem 37PS

Chapter 3.4, Problem 39PS

Chapter 3 Solutions

Calculus

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the rate (to the nearest hundredth gallons) at which water is leaking after 2 seconds.

Solution Summary: The author calculates the rate of change of Q(t) with respect to time.

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To find:the rate (to the nearest hundredth gallons) at which water is leaking after 2 seconds.

To find: the time it takesfor all the water to leak out of the bucket.

To find: the rate of water leakage when last drop leaks out.

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Chapter 3 Solutions