   Chapter 5.3, Problem 51E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Biology A population P of bacteria is growing at the rate of d P d t = 3000 1 + 0.25 t where t is the time (in days). When t = 0, the population is 1000.(a) Find a model for the population.(b) What is the population after 3 days?(c) After how many days will the population be 12,000?

(a)

To determine

To calculate: The model for the population P of bacteria that is growing at the rate of dPdt=30001+0.25t, when t=0, the population is 1000.

Explanation

Given Information:

A population P of bacteria is growing at the rate of

dPdt=30001+0.25t

When t=0, the population is 1000.

Where time (in days) is t.

Formula used:

The power rule of integrals:

undu=un+1n+1+C (for n1)

Here, u is function of x.

The property of Intro-differential:

df(x)dxdx=f(x)

Calculation:

A population P of bacteria is growing at the rate of

dPdt=30001+0.25t

Integrate both sides with respect to t.

dPdtdt=(30001+0.25t)dtP(t)=(30001+0.25t)dt

Consider the integration:

(30001+0.25t)dt

Rewrite the integration as:

30000.25(0.251+0.25t)dt

Let u=1+0.25t, then derivative will be,

du=d(1+0.25t)=0.25dt

Substitute du for 0

(b)

To determine

To calculate: The population P of bacteria after 3 days.

(c)

To determine

To calculate: The number of days require to reach bacteria population at 12,000.

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