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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

A bacteria population is 4000 at time t = 0 and its rate of growth is 1000 · 2t bacteria per hour after t hours. What is the population after one hour?

To determine

To calculate: The bacteria population after one hour duration.

Explanation

Given information:

The amount of bacterial population at time t=0 is r(0)=4,000bacteria.

Rate of growth of bacteria r(t) is (1,000×2t) bacteria per hour.

Calculation:

The expression for population growth of bacteria after t hours is shown below.

Population=r(0)+abr(t)dt (1)

Here, the initial bacterial population at time t0 is r(0), the rate of bacterial growth is r(t), the lower limit is a, and the upper limit is b.

Substitute 4,000 bacteria for r(0), 1,000×2t for r(t), 0 for a, and 1 hour for b in Equation (1) as shown below.

Population=4,000+01(1,000×2t)dt (2)

Integrate Equation (2) with respect to t and apply the limits

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