If I had a set of data and it followed a trend I would try to apply a function in your case possibly an exponential function.

Say if I had number of rats in a field at a given time per year

t = time in years

x = number of rats

I know what the initial number of rats= 20

so f(0) = 20

say if the function was the form of

where A is an constant

we apply x = 20 and t = 0 we get

so

therefore A = 20

by trail and error you could change the t variable to 2t or t/3 etc until it give an APPROXIMATE of your data you have

Your second problem you could apply differentiation so you would get the tangent a given time or if that isn't what your after you could just put a year Eg 1.5 into f(x) and you would get a return value of number of rats :]

Hope that helps you and i hope that answers your question.