Chapter 4.7, Problem 42E

Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Population Growth Fifty elk are introduced into a game preserve. It is estimated that their population will increase according to the model p ( t ) = 250 / ( 1 + 4 e − t / 3 ) , where t is measured in years. At what rate is the population increasing when t = 2 ? After how many years is the population increasing most rapidly?

To determine

To calculate: The rate of increase in the population of the elks when t=2 and the time when the population is increasing at the highest rate.

Explanation

Given:

The model that gives the population increase of elks at time t is:

p(t)=2501+4eâˆ’t3

Formula used:

For a function f that is twice differentiable on an open interval I, if f'(c)=0 for some c, then,

If f''(c)>0 the function f has relative minima at c if f''(c)<0 the function f has relative maxima at c.

Calculation:

Substitute 2 for t in the provided model to get rate of increase in the population of the elks when t=2.

p(2)=2501+4eâˆ’23=2501+4(0.5134)=2503

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Solve the inequality. 52. |x + 1| 3

Single Variable Calculus: Early Transcendentals, Volume I

In problems 63-73, factor each expression completely. 64.

Mathematical Applications for the Management, Life, and Social Sciences

Test the series for convergence or divergence. 9. n=1(1)nen

Single Variable Calculus: Early Transcendentals

Solve each inequality. 0x2+8

Trigonometry (MindTap Course List)