Chapter 4.6, Problem 23E

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

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**Population Growth** The number of a certain type of bacteria increases continuously at a rate proportional to the number present. There are 150 bacteria at a given time and 450 bacteria 5 hours later.

(a) How many bacteria will there be 10 hours after the initial time?

(b) How long will it take for the population to double?

(c) Does the answer to part (b) depend on the starting time? Explain your reasoning.

**(a)**

To determine

**To calculate:** The number of bacteria after

Explanation

**Given Information:**

The provided information is that there are

**Formula used:**

Exponential growth and decay:

If the rate of change of a positive quantity

If

**Calculation:**

Consider the provided information that there are

Let

Hence, an initial number of bacteria at

So,

Substitute

Now,

So, when

Substitute

**(b)**

To determine

**To calculate:** The time to double the population of bacteria if there are

**(c)**

To determine

If the time to double the population of bacteria as calculated in part (b) is dependent on the starting time provided that there are

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