Project 2: Exponential Curve Fitting

The equation for radio active decay is

y(t) = A exp(-rt),

as you know from calculus. The constant A represents the initial amount of the sample. We shall assume that the value of A is known exactly. The constant r is the decay rate. Suppose we have data from a sample and we wish to find r. You can check that if you know two data points exactly then r can be solved for exactly. However we shall add noise to the data. You are to adapt the least squares method to find the "best" value of r.

Reformulate this problem for population growth and for Newton's Law of Cooling.