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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 Because of an insufficient oxygen supply, the trout population P in a lake is dying. The population’s rate of change can be modeled by

d P d t = 125 e t / 20 where t is the time (in days). When t = 0, the population is 2500.

(a) Find a model for the population.

(b) What is the population after 15 days?

(c) How long will it take for the entire trout population to die?

(a)

To determine

To calculate: The model function for the trout population in lake that is growing at the rate of dPdt=125et/20, when t=0, the population is 2500.

Explanation

Given Information:

Consider population's rate of change,

dPdt=125et/20

When t=0, the population is 2500.

Where time (in days) is t.

Formula used:

The exponent rule of integrals:

eu(x)du(x)=eu(x)+C (for n1)

Here, u is function of x.

The property of Intro-differential:

df(x)dxdx=f(x)

Calculation:

Consider population's rate of change:

dPdt=125et/20

Integrate both sides with respect to t.

dPdtdt=(125et/20)dt+CP(t)=(125et/20)dt+C

Consider the integration:

(125e

(b)

To determine

To calculate: The population of trout after 15 days.

(c)

To determine

To calculate: The number of days require to die entire population.

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