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Math
CalculusCalculus (MindTap Course List)8th Edition

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Chapter 2.7, Problem 36E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

In a fish farm, a population of fish is introduced into a pond and harvested regularly. A model for the rate of change of the fish population is given by the equation

d P d t = r 0 ( 1 − P ( t ) P c ) P ( t ) − β+ P ( t )

where r0 is the birth rate of the fish, P c , is the maximum population that the pond can sustain (called the carrying capacity), and β is the percentage of the population that is harvested.

(a) What value of dP/dt corresponds to a stable population?

(b) If the pond can sustain 10, 000 fish, the birth rate is 5%, and the harvesting rate is 4%, find the stable population level.

(c) What happens if β is raised to 5%?

To determine

Part (a)

To find:

The value of dPdt corresponds to a stable population

Explanation

1) Given:

dPdt=r01- PtPcPt-ΒP(t)

2) Calculation:

Stable population means the population is not changing

Therefore,

For the stable population dPdt=0

⇒dPdt=r01- PtPcP

To determine

Part (b)

To find:

The stable population level

To determine

Part (c)

To find:

What happens when Β is raised to 5%

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Chapter 2.7,
Problem 35E
Chapter 2.8,
Problem 1E
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Mathematical Applications for the Management, Life, and Social Sciences

A result called Chebyshevs inequality states that for any probability distribution of an rv X and any number k ...

Probability and Statistics for Engineering and the Sciences

For Problems 5-54, perform the following operations with real numbers. Objectives 3-6 -12-7

Intermediate Algebra

The line x,y,z=0,0,0+n1,1,2 intersects the sphere x2+y2+z2=54 in two points. Find each point.

Elementary Geometry For College Students, 7e

Simplify: 4860

Elementary Technical Mathematics

For what value of k does the equation e2x=kx have exactly one solution?

Single Variable Calculus: Early Transcendentals

Free-Falling Object In Exercises 101 and 102. use the position function s(t)=16t2+500, which gives the height (...

Calculus of a Single Variable

Discounted short-term loans made to the U.S. government are known as U.S. Treasury_______. (10-13)

Contemporary Mathematics for Business & Consumers

Prove that the set of all roots of 1 forms a group with respect to multiplication.

Elements Of Modern Algebra

Arc Length The minute hand of a clock is 2 centimeters long. How far does the tip of the minute hand travel in ...

Trigonometry (MindTap Course List)

True or False? In Exercises 105108, determine whether the statement is true or false. If it is false, explain w...

Calculus: Early Transcendental Functions (MindTap Course List)

The graph of x = cos t, y = sin2 t is:

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

The angle θ at the right has cosine:

Study Guide for Stewart's Multivariable Calculus, 8th

A diagonal of a cube joins two vertices so that the remaining points of the diagonal lie in the interior of the...

Elementary Geometry for College Students

In Exercises 1-8, refer to the following matrices, and perform the indicated operations. Round your answers to ...

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding the Volume of a Solid In Exercises 3-12, use the shell method to write and evaluate the definite integr...

Calculus

Proof Prove that uv=uv if u and v are orthogonal.

Multivariable Calculus

Limit and Continuity In Exercises 11-24, find the limit and discuss the continuity of the function. lim(x,y)(0,...

Calculus (MindTap Course List)

A researcher wants to describe the effectiveness of a new program (compared to the old program) for teaching re...

Research Methods for the Behavioral Sciences (MindTap Course List)

Over forty states participate in Powerball, a lottery that requires choosing five of the number 1 through 59 an...

Mathematics: A Practical Odyssey

Using PsycINFO (or a similar database), find five articles on the topic of preschool daycare and social anxiety...

Research Methods for the Behavioral Sciences (MindTap Course List)

Benson Manufacturing is considering ordering electronic components from three different suppliers. The supplier...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Competition in the personal computer market is intense. A sample of 450 purchases showed 202 Brand A computers,...

Statistics for Business & Economics, Revised (MindTap Course List)

Backlash is the amount that a tooth Space is greater than the engaging tooth on the pitch circles of two gears....

Mathematics For Machine Technology

Critical Thinking Determine if the statement is true or false. If the statement is false, then correct it and m...

College Algebra (MindTap Course List)

Example 10.13 provided the following 21 time discrimination scores for male smokers who had abstained from smok...

Introduction To Statistics And Data Analysis

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