dPKAnother differential equation that is used to model population growch is called the Gompertz equation:dt= clnР.a. Solve this differential equation for e = 0.2, K = 3800 and initial population R = 600.-0.213800P =6003800b. Compute the limiting value of the size of the population.lim P(t) = 3800c. At what value of P does P grow fastest? That is, what is P when first derivative at a maximum and also where an inflection point occurs?3800d. For t > 0, determine the t-values where the graph of P is concave up and concave down. Enter your answers using interval notation. If there ismore than one interval, use capital U for union.Hint: You found the Pin which the change in concavity occur in Part c. How do you find the t-value?Concave up:Concave down:

Note: According to bartleby we have to answer only first question please upload the question…

cl Another differential equation that is used to model population growth is called the Gompertz equation: dt (수)» eIn a. Solve this differential equation for e = 0.2, K = 3800 and initial population P = 600. -0.2t 600 3800 3800

cl Another differential equation that is used to model population growth is called the Gompertz equation: dt (수)» eIn a. Solve this differential equation for e = 0.2, K = 3800 and initial population P = 600. -0.2t 600 3800 3800

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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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 differential equations.

Question

dP
K
Another differential equation that is used to model population growch is called the Gompertz equation:
dt
= cln
Р.
a. Solve this differential equation for e = 0.2, K = 3800 and initial population R = 600.
-0.21
3800
P =
600
3800
b. Compute the limiting value of the size of the population.
lim P(t) = 3800
c. At what value of P does P grow fastest? That is, what is P when first derivative at a maximum and also where an inflection point occurs?
3800
d. For t > 0, determine the t-values where the graph of P is concave up and concave down. Enter your answers using interval notation. If there is
more than one interval, use capital U for union.
Hint: You found the Pin which the change in concavity occur in Part c. How do you find the t-value?
Concave up:
Concave down:

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