# the expression for the number of bacteria after t , and estimate the rate of growth of the bacteria population after 2.5 hours. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 3.8, Problem 23E
To determine

## To find: the expression for the number of bacteria after t, and estimate the rate of growth of the bacteria population after 2.5 hours.

Expert Solution

Expression for growth of n bacteria in t hours is n(t)=400×3t.

The rate of growth of bacteria after 2.5 hours is 6,850units/hour.

### Explanation of Solution

Given:

The initial population n0 is 400.

Population of the bacteria triples in one hour as per the rate expression given below.

n(t)=n0×3t (1)

Calculation:

Expression for n bacteria in t hours.

Substitute the 400 for n0 in (2).

n(t)=400×3t (2)

Determine the rate of growth of population after 2.5 hours.

Differentiate equation (2) with respect to t.

dndt=400×3t(ln3)=400×3t(1.098)

dndt=439.44×3t (3)

Substitute 2.5 for t in equation (4).

dndt=439.44×32.5=6,850.19dndt6,850

Expression for growth of n bacteria in t hours is n(t)=400×3t.

The rate of growth of bacteria after 2.5 hours is 6,850units/hour.

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