Chapter 12.5, Problem 44E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Bacterial growth** Suppose that for a certain population of bacteria, growth occurs according to

If the doubling rate depends on temperature, find how long it takes for the number of bacteria to reach 50 times the original number at each given temperature in parts (a) and (b).

(a) At

(b) At

**(a)**

To determine

**To calculate:** The time required to reach number of bacteria 50 times the original number at

Explanation

**Given Information:**

The certain population of bacteria, growth occurs according to

If the doubling rate depends on the temperature,

The bacteria will be double after 30 minute.

**Formula used:**

The differential equation can be equivalently expressed in the form

Then the equation is separable.

The solution of a separable differential is obtained by integrating both sides of the equation after the variable have been separated.

**Calculation:**

Consider the certain population of bacteria, growth occurs according to

If the doubling rate depends on the temperature,

Firstly, separate the above differential equation as:

Integrate the provided function as:

At the given condition

**(b)**

To determine

**To calculate:** The time required to reach number of bacteria 50 times the original number at

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