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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Biology A lake is stocked with 500 fish, and the fish population P begins to increase according to the logistic growth model

P = 10 , 000 1 + 19 e 1 / 5 ,   t 0 where t is the time in months.

(a) Find the number of fish in the lake after 4 months.

(b) Use a graphing utility to graph the model. Find the number of months it takes for the population of fish to reach 4000.

(c) Does the population have a limit as t increases without bound? Explain your reasoning.

(a)

To determine

To calculate: The number of fishes in the lake after 4 months when the lake consists of 500 fishes in starting and the fish population P increases with time t (in months) is given by the logistic growth model as,

P=10,0001+19et5

Explanation

Given Information:

The lake consists of 500 fishes in starting and the fish population P increases with time t (in months) is given by the logistic growth model as,

P=10,0001+19et5

Calculation:

Consider that the lake consists of 500 fishes in starting and the fish population P increases with time t (in months) is given by the logistic growth model as,

P=10,0001+19et5

Compute the number of fishes in the lake after 4 months by substituting t=

(b)

To determine

To graph: The model by using technology which represents the fish population P increases with time t (in months) is given by the logistic growth model as,

P=10,0001+19et5

Also determine the number of months required in order that the population of the fishes reaches to 4000.

(c)

To determine

Whether the limit of population of the fishes in the lake have some value or not as t increases without bound and give reason when the fish population P increases with time t (in months) is given by the logistic growth model as,

P=10,0001+19et5

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