% Clear all variables, close all windows, clear screen
clear all; close all; clc;

% Data points
t = [0 5 10 15 20 25];
b = [100 200 450 950 2000 5000];

% Linearised data points
x = t;
y = log(b);

% Calculates the line
coefficients = polyfit(x,y,1);
a1 = coefficients(1);
a0 = coefficients(2);

% Converts back to original curve
alpha = exp(a0);
beta = a1;

% Function to plot
range = @(domain) alpha.*exp(beta.*domain);

% Extrapolated values
extrapX = 30;
extrapY = range(extrapX);

% Plots the first figure according to the correct format
plot(t,b,'kd')
hold on
plot(extrapX,extrapY,'ro');
legend('Bacteria','Extrapolated data point','location','northwest');
fprintf('At t = %f, extrapolated data point: %f',extrapX,extrapY);
xlabel('Time (minutes)');
ylabel('Bacteria');
title('Bacteria vs Time')
legend('Raw data','Extrapolated data point','location','northwest')
fprintf('\na0: %f\na1: %f\n',a0,a1);

% Sets the domain and order of polynimial with user input
domain = linspace(0,30,60);
n = input('\nEnter degree of polynomial: ');
coefficientsp = polyfit(t,b,n);
extrapYp = polyval(coefficientsp,extrapX);

% Creates new figure
% Plots the second polynomial figure
figure();
plot(domain,polyval(coefficientsp,domain));
hold on
plot(extrapX,extrapYp,'ro');
hold on
legend('Polynomial fit','Extrapolated data point','location','northwest');
fprintf('At t = %f, extrapolated data point: %f\n',extrapX,extrapYp);
xlabel('Time (minutes)');
ylabel('Bacteria');
title(sprintf('Bacteria vs Time (degree of %d)', n));