%Written by: Taylor Poon, ID: 30750539
%Created: 18/09/19
%yeasty bacteria growth rate that produces an antibiotic
clear all; close all; clc;

%root finding equation
%anonymous function for yeasty boi equation
g = @ (c) 2.*c./(4+0.8.*c+c.^2+0.2.*c.^3);
dg = @ (c) 10*(20 - 5*c.^2 - 2*c.^3)./((c + 5).^2.*(c.^2+4).^2);

%determine value of c where growht is maximum using false position method
cl = 0; %change bounds as they are inappropriate?
cu = 5;
precision = 1e-4;
[root,iter] = falseposition(dg, cl, cu, precision);

%plots
c = linspace(0,10);
%plot: g against c
plot(c, g(c))
title('Yeasty Boi Function');
xlabel('food concentration (mg/L)');
ylabel('specific growth rate (day^-1)');
%plot: g' against c
hold on
plot (c, dg(c), 'k')

%plot: vertical line
xline(root, 'r');
legend('g against c', 'dg against c', 'vertical line at solution')

%print statement
fprintf('The value of the concentration when the growth is a maximum is %f, and the numer of iterations using the false position method was %0.f.', root, iter);