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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1, Problem 28RE

(a)

To determine

**To estimate:** The time taken in which the population reaches 900 with the help of graph of the given equation.

Expert Solution

**Solution:**

The time taken in which the population to reach 900 is approximately 4.4 years.

**Given:**

The initial population in an limited environment is 100 with the carrying capacity 1000.

Also the population at any instant of time *t* is,

**Graph:**

Use online graph calculator and draw the graph of the function

From Figure1,obtain that point of intersection of the graph of

Therefore, time taken by the population to reach 900 is approximately 4.4 years.

(b)

To determine

**To find:** The inverse of the given function and to explain its meaning.

Expert Solution

**Solution:**

The inverse of the function is *P.*

**Calculation:**

Let

Again solve the above equation,

Take reciprocal on both sides,

Take natural logarithm on both sides,

Since

Therefore,

Where *t* is the inverse of the function and *t* denotes the time taken by the population to reach *P.*

(c)

To determine

**To find:** The time required by the population to reach 900 by using the inverse function.

Expert Solution

**Solution:**

The time required for the population to reach 900 by using the inverse function is approximately 4.39 years.

**Calculation:**

From part(b), the inverse of the function is

Given that

Therefore, the inverse of the function is,

Thus, the time required for the population to reach 900 by using the inverse function is approximately 4.39 years.

Compare this answer with the answer in part (b) and observe that the answers are approximately same.