%%% Clean up workspace 
clear vars 
 
%%%variables 
tspan = [0:0.01:1];
K = 10; 
y0 = 2;
r = 2; 
 
%%% Population growth ODE solution 
[t,y] = ode45(@(t,y) y0*K/(y0+(K-y0)*exp(-r*t)), tspan, y0);
 
%%% Plot of solution 
plot(t,y,'-o')
 
%% Plot other paths 
hold on
 
r = 0.5; 
 
[t,y] = ode45(@(t,y) y0*K/(y0+(K-y0)*exp(-r*t)), tspan, y0);
 
plot(t,y,'-o')
 
hold on 
 
r = 1.0;
 
[t,y] = ode45(@(t,y) y0*K/(y0+(K-y0)*exp(-r*t)), tspan, y0);
 
plot(t,y,'-o')
 
hold on 
 
r =1.5;
 
[t,y] = ode45(@(t,y) y0*K/(y0+(K-y0)*exp(-r*t)), tspan, y0);
 
plot(t,y,'-o')