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6th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285774770

Chapter 6.4, Problem 13E

Textbook Problem

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Using a Logistic Differential Equation In Exercises 15-18, the logistic differential equation models the growth rate of a population. Use the equation to (a) find the value of k , (b) find the carrying capacity, (c) use a computer algebra system to graph a slope field, and (d) determine the value of P at which the population growth rate is the greatest.

**(a)**

To determine

**To calculate:** The value of *k* of the logistic differential equation

**Given:**

The logistic differential equation

**Formula used:**

The general logistic differential equation is

**(b)**

To determine

**To calculate:** The value of carrying capacity of the logistic differential equation

**(c)**

To determine

**To graph:** The slope field of the logistic differential equation

**(d)**

To determine

The value of *P* at which the population growth rate is greatest for the logistic differential equation d P d t = 3 P ( 1 − P 100 )

Calculus: Early Transcendental Functions (MindTap Course List)

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Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential...Ch. 6 - Solving a First-Order Linear Differential...Ch. 6 - Solving a First-Order Linear Differential...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Slope Field In Exercises 67-70, (a) sketch an...Ch. 6 - Slope Field In Exercises 67-70, (a) sketch an...Ch. 6 - Slope Field In Exercises 67-70, (a) sketch an...Ch. 6 - Slope Field In Exercises 67-70, (a) sketch an...Ch. 6 - Finding a Particular Solution In Exercises 71-74,...Ch. 6 - Finding a Particular Solution In Exercises 71-74,...Ch. 6 - Writing In Exercises 6769. write an example of the...Ch. 6 - Writing In Exercise 6769. write an example of the...Ch. 6 - Writing In Exercises 6769, write an example of the...Ch. 6 - Investment Let A(t) be the amount in a fund...Ch. 6 - Investment A retired couple plans to withdraw P...Ch. 6 - Investment Use the result of Exercise 70 to find...Ch. 6 - Analyzing Predator-Prey Equations In Exercises 79...Ch. 6 - Analyzing Predator-Prey Equations In Exercises 79...Ch. 6 - Analyzing Competing-Species Equations In Exercises...Ch. 6 - Analyzing Competing-Species Equations In Exercises...Ch. 6 - Doomsday Equation The differential equation where...Ch. 6 - Sales Let S represent sales of a new product (in...Ch. 6 - Error Using the Product Rule Although it is true...Ch. 6 - Torricellis Law Torricellis Law states that water...Ch. 6 - Torricelli's Law The cylindrical water tank shown...Ch. 6 - Torricelli's Law A tank similar to the one in...Ch. 6 - Rewriting the Logistic Equation Show that the...Ch. 6 - Biomass Biomass is a measure of the amount of...Ch. 6 - Finding a Function Consider a function f such that...Ch. 6 - If the tracer is injected instantaneously at time...Ch. 6 - Use the solution of the differential equation in...Ch. 6 - 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