Problem 1 as reference. Asking for solution to problem 2 gisse) d dP2. Consider the logistic differential equation = A(C-P)P with C = 100dt(0) and A = 0.005. For 0 < t < 10 sketch the graphs of the particular solutionsthat satisfy the given initial conditions. Use a graphing calculator orsoftware for graphing and formulas from Exercise 1.(a) P(0) = 125 (b) P(0) = 75 (c) P(0) = 10. Cae-CAt +11. (a) Verify that P(t)dPequation = A(C - P)P. Here a is an arbitrary constant.dt=is a solution of the logistic differential(b) Obtain the formula for P(t) by solving the logistic differential equa-tion.P(0) = Po.(c) Solve the initial value problem = A(C - P)P,dPdt

Answered: dP 2. Consider the logistic…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Problem 1 as reference. Asking for solution to problem 2

gisse) d dP
2. Consider the logistic differential equation = A(C-P)P with C = 100
dt
(0) and A = 0.005. For 0 < t < 10 sketch the graphs of the particular solutions
that satisfy the given initial conditions. Use a graphing calculator or
software for graphing and formulas from Exercise 1.
(a) P(0) = 125 (b) P(0) = 75 (c) P(0) = 10.

C
ae-CAt +1
1. (a) Verify that P(t)
dP
equation = A(C - P)P. Here a is an arbitrary constant.
dt
=
is a solution of the logistic differential
(b) Obtain the formula for P(t) by solving the logistic differential equa-
tion.
P(0) = Po.
(c) Solve the initial value problem = A(C - P)P,
dP
dt

Expert Solution

Step 1

What is Logistic Growth:

When there are fewer people, population growth occurs slowly at first, then picks up speed as the population grows, and finally slows to a stop as the population reaches a point at which resources run out and further population growth is impossible. The graph of logistic growth shows an S-shaped curve (S curve).

Given:

Given logistic equation is,

$\frac{d P}{d t} = A (C - P) P$ .

Given that,

$A = 0.005, C = 100$ .

To Determine:

We sketch the graph of the particular solution under the initial conditions

$\begin{array}{rcl} P (0) & = & 125 \\ P (0) & = & 75 \\ P (0) & = & 10 \end{array}$ .