A logistic growth model can be used model population growth when there are limited resources to support the population. For instance, the model can be used to track the population growth of a species of fish in a pond, where the limited space and availability of food will place constraints on how the fish population can increase in time. Epidemic dynamics can use the same model to predict the cumulative number of cases when the primary method of control is quarantine, as is the case in many novel viral infections, including the COVID-19 outbreak. Problem The differential equation that models logistic growth is -ax(1-#). NP = kN dt where N(t) is the cumulative number of infected cases at time t, k is the infection rate, and L is a constant. For the purpose of this problem, we will take L = 20 and k = 1/4. П. Substitute the values for k and L into the equation and show that the differential equation can be 80 brought into the form dN = dt. N(20 - N) III. Solve the initial value problem dN = dt, N(0) = 2 by integrating the left and righthand N(20 -. - N) sides. Explicitly solve for N in your final answer. IV. Use your answer to Part III to calculate lim N(t).

A logistic growth model can be used model population growth when there are limited resources to support the population. For instance, the model can be used to track the population growth of a species of fish in a pond, where the limited space and availability of food will place constraints on how the fish population can increase in time. Epidemic dynamics can use the same model to predict the cumulative number of cases when the primary method of control is quarantine, as is the case in many novel viral infections, including the COVID-19 outbreak. Problem The differential equation that models logistic growth is -ax(1-#). NP = kN dt where N(t) is the cumulative number of infected cases at time t, k is the infection rate, and L is a constant. For the purpose of this problem, we will take L = 20 and k = 1/4. П. Substitute the values for k and L into the equation and show that the differential equation can be 80 brought into the form dN = dt. N(20 - N) III. Solve the initial value problem dN = dt, N(0) = 2 by integrating the left and righthand N(20 -. - N) sides. Explicitly solve for N in your final answer. IV. Use your answer to Part III to calculate lim N(t).

Name: See picture for question A logistic growth model can be used model pop
Uploaded: 2024-03-20T06:46:14.000Z
Channel: Bartleby
Description: See picture for question A logistic growth model can be used model population growth when there are limited resourcesto support the population. For instance, the model can be used to track the population growth of a species of fish ina pond, where th

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 16EQ

See similar textbooks