function N=population(A,N0,T,maxN)
% function N=population(A,N0,T,maxN)
%
% A is a parameter vector to be passed on to ratefnc.
%
% This function calculates the population up to time T
%  for the differential equation N'=ratefnc(N) with N_0=N0.
%
% maxN is the largest value of N for the plots.


% define the parameters

R = A(1);
K = A(2);

% compute the population values using Matlab's standard ODE solver.

trange=[0 T];
[t,N] = ode45(@ratefnc,trange,N0);

% plot the computed points (t,N) as a smooth curve.  Set the axis ranges and labels.

plot(t,N)
xlim([0,T])
ylim([0,maxN])
xlabel('\it{t}','FontSize',12)
ylabel('\it{N}','FontSize',12,'Rotation',0)

% the code that follows is used to compute the new population levels
% the parameters need to have been defined earlier

    function f=ratefnc(t,N)
        f = R*N*(1-N/K);
    end

end