Logistic Growth Model - Code and Plot

I need to plot a differential equation that shows logistic growth. The equation is: P=(K*A*e^r*t)/(1+A*e^r*t)

where K is the carrying capacity, a constant, and K = 1,704,885 and A = 0.0122.

I need the correct code so that I can solve for r, as well as put different t to find the population at varying times.

I also need to plot the solution. Thank you for any help!

Answer 1

[Jaswanth]

Hi,

The following example code can help you solve the logistic growth equation for different values of time t, given the carrying capacity K, the constant A, and the growth rate r. It also plots the population P over time.

% Define constants
K = 1704885; % Carrying capacity
A = 0.0122;  % Constant
r = 0.1;     % Growth rate (you can adjust this value as needed)

% Define the time vector
t = linspace(0, 100, 1000); % Time from 0 to 100 in 1000 steps

% Calculate the population P at each time t
P = (K * A .* exp(r .* t)) ./ (1 + A .* exp(r .* t));

% Plot the solution
figure;
plot(t, P, 'b-', 'LineWidth', 2);
xlabel('Time');
ylabel('Population');
title('Logistic Growth');
grid on;

To solve for different values of r, you can adjust the value of r in the example and re-run it. I hope the information provided above is helpful.