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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The population of a certain species in a limited environment with initial population 100 and carrying capacity 1000 is

P ( t ) = 100 , 000 100 + 900 e t

where t is measured in years.

(a) Graph this function and estimated how long it takes for the population to reach 900.

(b) Find the inverse of this function and explain its meaning.

(c) Use the inverse function to find the time required for the population to reach 900. Compare with the result of part (a).

(a)

To determine

To estimate: The time taken in which the population reaches 900 with the help of graph of the given equation.

Explanation

Given:

The initial population in an limited environment is 100 with the carrying capacity 1000.

Also the population at any instant of time t is, P(t)=100,000100+900et.

Graph:

Use online graph calculator and draw the graph of the function P(t)=100,000100+900et when P(t)=900

(b)

To determine

To find: The inverse of the given function and to explain its meaning.

(c)

To determine

To find: The time required by the population to reach 900 by using the inverse function.

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