Explanation Result used: Logistic equation d P d t = k P ( 1 − P M ) (1) Here M is carrying capacity Solution of logistic equation is, P ( t ) = M 1 + A e − k t Where A= M − P 0 P 0 (2) Calculation: Consider the equation d y d t = 2 y ( 1 − y 5 ) , which is in the form of logistic equation, where the carrying capacity is M = 5 and k = 2 Substitute the value of M and k in equation (2) Compute the value of A as follows, A = 5 − 1 1 = 4 Substitute the value of A , M and k in equation (2) P ( t ) = 5 1 + A e − 2 t

8th Edition

ISBN: 9781305266636

Author: James Stewart

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 9, Problem 7RQ

To determine

Whether the statement “If y is the solution of the initial-value problem

dydt=2y(1−y5), y(0)=1 then limt→∞y=5” is true or false.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9, Problem 6RQ

Chapter 9, Problem 1RE

Students have asked these similar questions

Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)

There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three investment? STEP 1: The formula for compound interest is A = nt = P(1 + − − ) n², where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to A = Pert Find r and n for each model, and use these values to write A in terms of t for each case. Annual Model r=0.10 A = Y(t) = 1150 (1.10)* n = 1 Quarterly Model r = 0.10 n = 4 A = Q(t) = 1150(1.025) 4t Continuous Model r=0.10 A = C(t) =…

Use a graphing utility to find the point of intersection, if any, of the graphs of the functions. Round your result to three decimal places. (Enter NONE in any unused answer blanks.) y = 100e0.01x (x, y) = y = 11,250 ×

Chapter 9 Solutions

Single Variable Calculus

Ch. 9.1 - Show that y=23ex+e2x is a solution of the...Ch. 9.1 - Verify that y = t cos t t is a solution of the...Ch. 9.1 - (a) For what values of r does the function y = erx...Ch. 9.1 - (a) For what values of k does the function y = cos...Ch. 9.1 - Which of the following functions are solutions of...Ch. 9.1 - Prob. 6E Ch. 9.1 - (a) What can you say about a solution of the...Ch. 9.1 - (a) What can you say about the graph of a solution...Ch. 9.1 - A population is modeled by the differential...Ch. 9.1 - The Fitzhugh-Nagumo model for the electrical...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Whether the statement “If y is the solution of the initial-value problem d y d t = 2 y ( 1 − y 5 ) , y ( 0 ) = 1 then lim t → ∞ y = 5 ” is true or false.

Solution Summary: The author evaluates whether the statement "If y is the solution of the initial-value problem" is true or false.

Concept explainers

Videos

Whether the statement “If y is the solution of the initial-value problem

dydt=2y(1−y5), y(0)=1 then limt→∞y=5” is true or false.

Want to see the full answer?

Chapter 9 Solutions

Whether the statement “If y is the solution of the initial-value problem d y d t = 2 y ( 1 − y 5 ) , y ( 0 ) = 1 then lim t → ∞ y = 5 ” is true or false.

Solution Summary: The author evaluates whether the statement "If y is the solution of the initial-value problem" is true or false.

Concept explainers

Videos

Whether the statement “If y is the solution of the initial-value problem dydt=2y(1−y5), y(0)=1 then limt→∞y=5” is true or false.

Want to see the full answer?

Chapter 9 Solutions

Whether the statement “If y is the solution of the initial-value problem

dydt=2y(1−y5), y(0)=1 then limt→∞y=5” is true or false.