(a) Explanation Given: Polluted fluid from a factory begins to enter a lake at the rate: f ( t ) = 8 ( 1 − e − 0.25 t ) where t is the time (in hours), and f ( t ) is in gallons per hour. At the same time, a pollution filter begins to remove the pollution at the rate of: g ( t ) = 0.2 t , where t is the time in hours, and g ( t ) is in gallons per hour. Formula used: If f ( x ) and g ( x ) are curve and to calculate the area between curve over interval x = a to x = b and f ( x ) ≥ g ( x ) in the provided interval then the area is; ∫ a b [ f ( x ) − g ( x ) ] d x Here f ( x ) , g ( x ) are the rate at which pollution fluid is entering and removing respectively (b) To determine To calculate: The time at which the rate of pollution enters the lake equal the rate of pollution is being removed. (c) To determine To calculate: the pollution is in the lake at the time found in part (b). (d) To determine To calculate: The time at which all the pollution will be removed from the lake

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

11th Edition

ISBN: 9780321931078

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 13.5, Problem 29E

(a)

To determine

To calculate: The pollution is in the lake after 20 hours.

(b)

To determine

To calculate: The time at which the rate of pollution enters the lake equal the rate of pollution is being removed.

(c)

To determine

To calculate: the pollution is in the lake at the time found in part (b).

(d)

To determine

To calculate: The time at which all the pollution will be removed from the lake

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Chapter 13.5, Problem 28E

Chapter 13.5, Problem 30E

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Chapter 13 Solutions

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - Prob. 9CP Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...

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