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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.8, Problem 24E

To determine

**To find:** The value of

Expert Solution

The value of

The yeast will reach the population of 140 for the long run.

**Given:**

The population is modelled by a function as below.

Differentiate (1) with respect to

At time

Increase rate of population with respect to time is given as below.

**Calculation:**

Equate the equation (4) and (2).

Substitute 0 for

Equate equation (4) and (3).

Determine the value of

Equate equation (4) and (5).

Substitute

The value cannot be negative.

Therefore, the value of

Determine the value of

Substitute 6 for

Therefore, the value of

Hence the value of

Determine the yeast population

For the population in long run take time

Hence the yeast will reach the population of 140 in the long run.

The value of

The yeast will reach the population of 140 for the long run.