Why the graph is not look like logistic graph?

Hi, I have a problem in plotting logistic model graph. May I know what is the problem of my coding and how to solve it? I would be grateful that the answer that provided. Thanks!

Here is the source code:

%% Initialize Input
K = 100000000; % Carrying Capacity of Brain Tumor
C0 = 40000; % Initial Brain Tumor Population Size
r = 4.31*(10^-3); % Growth Rate of Brain Tumor Cells

%% Model Data
t = 730; % Time in Days
C = zeros(t,1) ;
C(1) = C0;
lastArray = {};
% Calculating Brain Tumor Population 
for i=1:1:t-1
    C(i+1) = (K*(C0*exp(r*i)))/(K-C0+C0*exp(r*i));
end
c=cumsum(C);
hold on
nvec = 1:1:t;

%% Graph Plotting
figure(1)
title( 'Brain Tumor Population Against Time' )
xlabel('Time (Days)')
ylabel('Brain Tumor Population (cells)')
plot(nvec,cumsum(C),'--bo','LineWidth',0.5,'MarkerSize',5,'MarkerEdgeColor','black')
grid
hold on

Here is the output:

Answer 1

[Cris LaPierre]

The most likely reasons are 1) you have not gone out far enough in x or 2) you have not written a logistic expression.

Note that r must be negative to have your logistic increase asymptotically, and >0 to decrease asymptotically to 0. Perhaps you just need to put a negative in front of r?

%% Initialize Input
K = 100000000; % Carrying Capacity of Brain Tumor
C0 = 40000; % Initial Brain Tumor Population Size
r = 4.31*(10^-3); % Growth Rate of Brain Tumor Cells

%% Model Data
t = 0:730; % Time in Days

% Calculating Brain Tumor Population 
C = K*C0*exp(-r*t)./(K-C0+C0*exp(-r*t));

%% Graph Plotting
plot(t,cumsum(C),'--bo','LineWidth',0.5,'MarkerSize',5,'MarkerEdgeColor','black')
title( 'Brain Tumor Population Against Time' )
xlabel('Time (Days)')
ylabel('Brain Tumor Population (cells)')
grid

Still, I don't believe you should have to use a cumsum to get the results, and they still don't look like a typical logistic plot, so perhaps check your equation? For example, here's an equation that I think is more typical of logistic growth.

At , C=C0 and at , C=K. It is also able to obtain the expected results without using cumsum. I do make it go to 1400 to see the assymptote.

%% Initialize Input
K = 100000000; % Carrying Capacity of Brain Tumor
C0 = 40000; % Initial Brain Tumor Population Size
r = 4.31*(10^-3); % Growth Rate of Brain Tumor Cells

%% Model Data
t = 0:1400; % Time in Days

% Calculating Brain Tumor Population 
C = K*(C0/K).^exp(-r*t);

%% Graph Plotting
figure
plot(t,C,'--bo','LineWidth',0.5,'MarkerSize',5,'MarkerEdgeColor','black')
title( 'Brain Tumor Population Against Time' )
xlabel('Time (Days)')
ylabel('Brain Tumor Population (cells)')
grid

[Deck Zhan Sim]

I managed to get it already. Thanks for helping!