clear all;      % good to start by clearing all old variables
alpha = 0.2;    % alpha will be rate of decay, one-over-the-timeconstant
dt=0.001;       % time-step size: always check if making it smaller affects the results
T=0:dt:10;      % T is a vector from 0 to 10 in steps of dt --- in this case 10001 elements
xstart = 100.0; % this will be the initial value of x --- where x starts from
x=zeros(size(T)); % x is a vector the same as T but with every element set to zero
x(1) = xstart;  % now the first element in x is set to xstart. This corresponds to a time of zero since T(1)=0
for ( i = 2: length(T) )  % beginning of a loop with i =2 first time, then 3, then 4 ... until i = 10001 as length(T)=10001
    x(i) = x(i-1) - x(i-1)*dt*alpha; % change in x is -x*dt*alpha solves the eqn: dx/dt = -alpha*x
end             % end of for loop, so go back to line 8 unless i has reached 10001 already
x(end)          % this just prints out the last value of x

figure(1);      % start a figure called figure(1)
plot(T,x);      % plot x against T