Given that you have to use AB2 (with, apparently, a fixed stepsize) I going to take a guess that this is a numerical analysis homework problem? (If not, use one of the built-in MATLAB linear multistep methods, such as ode113.)
For fixed stepsize, you can calculate all the t values immediately. Look at either the linspace function or the range operator (:).
You can and should make room for the u values before you start to calculate them. Look at zeros.
Set the first value of u from the initial condition.
Loop to fill in the rest of the values, based on the previous ones. Given that you know how many steps you're going to take, use a for-loop.
You can hard-code the rate equation inside your loop if you like. But if you want to be a bit fancier, use an anonymous function handle to define it. Something like f = @(x,y) -2*y + ... Then you can evaluate it anywhere later by simply calling f(t(k),y(k)) (or whatever).
