% This is the main function to solve 
% dN/dt = KN in p.117, Mathematical Models in Biology


global K

K = 1; % rate of reproduction per unit time
options = odeset('RelTol',1e-4,'AbsTol',1e-4);
t0 = 0;
tfinal = 3;
N_ini = 5;
[T,N] = ode45(@bacterialgrowth,[t0 tfinal],N_ini,options);

% plot N at different T
plot(T,N)
xlabel t, ylabel N


% plot exact solution

Nexact = N_ini*exp(K*T);

figure(2)
plot(T,Nexact,'r')
xlabel t, ylabel('exact solution of N')