How to write a program that produces bifurcation diagrams?

We want to write a program in MATLAB for the function: p(t+1) = f_alpha(p(t)) = alpha*p(t)*e^(-p(t)), alpha > 0. The program has to produce a plot for a given interval [alpha_min,alpha_max] (which are positive real numbes) and initival value p0 >= 0 with the approximate positive limit points of p0. We have to choose a p0 > 0 and use our program to plot the positive limit points for the initial values 0 and p0 with alpha between 0 and 12.

After that, we have to generalize our porgram in such a way that it can produce bifurcation diagrams. That is, for each alpha it should plot the positive limit points of sufficiently many initial values, where the initial values should be chosen smartly. Construct this bifurcation diagram for [alpha_min,alpha_max]=[0,16].

We really don't know how to start...