If T=.23L^.48 and that is a constant then can those numbers always be put into any equation, like T=A*L^p?
y = A x^p is the general form of a power function y of the independent variable x.
Our pendulum period vs. length function uses variables T and L instead of y and x.
So T = A * L^p is the general form of a power function T of the independent variable L.
Knowing that the pendulum period should be a power function of its length, we would then know to use the form T = A * L^p. If we know the values of T at two different values of L, we can then substitute each pair of values into the form to get an equation in the parameters A and p (see notes from late in the first week for specific examples of this).
Once we have two equations in A and p, we can solve them for A and p.
Having obtained our values of A and p, we then plug them into the form T = A * L^p, giving us our mathematical model of period T as a function of length L.
The model we got from our observations in class (again see notes from week 1) is pretty close to T = .23 L^.48.
The ideal model given by physics is T = .20 L^.50. So we did pretty well.