If P(t) satisfies the logistic equation in (3), use the chain rule to show that Conclude that

Question:

If P(t) satisfies the logistic equation in (3), use the chain rule to show that

Conclude that P'' > 0 if 0 0 if P > M. In particular, it follows that any solution curve that crosses the line P = 1/2M has an inflection point where it crosses that line, and therefore resembles one of the lower S-shaped curves in Fig. 2.1.3.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Differential Equations And Linear Algebra

ISBN: 9780134497181

4th Edition

Authors: C. Edwards, David Penney, David Calvis

See More Books

Question Posted: Jun 27, 2023 09:32 AM

See More Questions

Two judges at a college homecoming parade rank 8 floats in the following order:(a) Calculate the rank correlation.(b) Test the null hypothesis that p = 0 against the alternative that p > 0. Use a...
You are required to prepare/submit an individual report discussing the following: Choose a Multinational Enterprise (MNE) listed on an internationally recognized Stock Exchange (including for...
Use the Chain Rule to show that if is measured in degrees, then (This gives one reason for the convention that radian measure is always used when dealing with trigonometric functions in calculus: The...
Carbon has the electron configuration 1s 2s2p. The two unpaired electrons in the n = 2 level suggests that carbon will form two bonds. We know, however, that carbon forms four bonds in most compounds...
Information taken from a Sears, Roebuck and Company annual report follows. Required 1. How much interest expense did the company record during Year 2 on the 7% debentures? How much of the original...
Gletchen Cough Drops operates two divisions. The following information pertains to each division for 2018. Required a. Compute each division's residual income. b. Which division increased the...
FRAUD PREVENTION AND DETERRENCE IN ACTION Assume the following facts: thirty-day collection period. The invoice is used to post-sales to the accounting system. Checks are received in the mailroom and...
Presented below is information for Furlow Company for the month of March 2014. Instructions (a) Prepare a multiple-step income statement. (b) Compute the gross profitrate. Cost of goods sold...
As an example of how simulation can be used for operations research, consider the following college enrollment model. A certain college wants to analyze the effect of admissions and freshman...
The Rabbit-fox-and some other animal Simulation 100 points possible Implement exercise 12.51 by adding a third animal to the rabbit and fox simulation. The third animal must interact with the fox and...
The data in the table in Fig. 2.1.7 are given for a certain population P(t) that satisfies the logistic equation in (3). (a) What is the limiting population M? (Suggestion: Use the approximation with...
(a) Derive the solution of the extinction-explosion initial value problem P' = kP(P - M), P(0) = P 0 .(b) How does the behavior of P(t) as t increases depend on whether 0 0 0 > M? P(t)= MPo Po...
Complete the following table. Inventory at cost ($) Mark-up ($) Inventory at transfer price (S) 12 000 20 26 000 40 ? 25 50 000 ? 10 33 000
Decide whether the system in Problem 1 is stable. A linear dynamic system is stable if the homogeneous solution of its mathematical model, subjected to the prescribed initial conditions, decays. More...
When rolling a single die, what is the probability that the outcome is 7?
When guessing the answer to a multiple-choice question on an SAT test, the chance of guessing correctly is 1 in 5. Express the indicated degree of likelihood as a probability value between 0 and 1.
Given that the following statement is incorrect, rewrite it correctly: The probability of a baby being born a boy is 5050.
Based on a Harris poll, there is a 5050 chance that a randomly selected adult has pierced ears. Express the indicated degree of likelihood as a probability value between 0 and 1.
Avery, Inc., manufactures two component parts for the television industry: Tvez. Annual production and sales of 50,000 units at a selling price of $48.72 per unit. Premia. Annual production and...
In July 2013, cnet.com listed the battery life (in hours) and luminous intensity (i. e., screen brightness, in cd/m2) for a sample of tablet computers. We want to know if screen brightness is...
Other Bases: Use the Solution Space Theorem to show that the sets given in Problems 1 and 2 are each a basis for the DE? 1. y' - 4y = 0; {e2t, e-2t}, {cosh 2t, sinh 2t}, {e2t, cosh 2t} 2. y" = 0; {1,...
The Wornskian Test: Use the Wronskian Test in Problems 1-3 to determine if the set of solutions is a basis for the given DE. 1. y(4) = 0, {t + 1, t - 1, t2 + t, t3} 2. y" - 10 y" - 15y' = 0. {te-5t,...
Sorting Graphs: For the DE + 5+ 6x = 0 of Example 1, Fig. 4.2.8 adds to Fig. 4.2.1 the linked solution graph for (t). Label the phase-plane trajectories from left to right as A, B, C. D, E. Then...
To reduce heat transfer to a 6.0-m-long copper (k = 380 WmK) refrigerant line of 0.50 cm inside diameter and 0.60 cm outside diameter, a plumber recommends that you insulate the line with a...
Which one of the following best explains why an insurer would prefer to issue surplus notes rather than bonds to raise capital? Available answer options Select only one option A Bonds are classified...
a) A tensile test can be used to generate a stress-strain curve and to determine a variety of material properties. List four properties that can be deduced from a stress strain- curve. [4 marks] b)...

If P(t) satisfies the logistic equation in (3), use the chain rule to show that Conclude that

Question:

P"(t)=2k² P(P-M)(P-M).

Step by Step Answer:

Differentiation of both sides of ...View the full answer

Differential Equations And Linear Algebra

Students also viewed these Mathematics questions