% simulate the growth of volume of a bacterial cell depending on a constant
% growth rate.

clear all;

%declare the constants

k=1;
nutrient = 21;  %concentration of nutrient
n = 0.8;
Ka = 10.5;
theta = (nutrient^n) / (((Ka)^n) + (nutrient^n));   %The Hill function
t=[0.01:0.01:10];       %Declaring the time span
%create graph

v1=exp(k*t);        %The Analytical solution for constant growth
v=exp((theta)*t);   %The Analytical solution for growth including the Hill
                    %function

subplot(2,1,1);
plot(t,v); grid on;
xlabel('time'); ylabel('volume of the cell');
title('An ODE model for the growth of the cell volume depending on a constant growth rate');

subplot(2,1,2);
plot(t,v1); grid on;
xlabel('time'); ylabel('volume of the cell');
title('An ODE model for the growth of the cell volume incorporating the hill function');
