BuyFind

Single Variable Calculus: Concepts...

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

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

Answer to Problem 23E

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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