Question

Suppose that for some values of A and r, P(t)=Ae^rt and we know that P(8)=175 and P(11)=125. Find A and r.

Answer 1

175 = A * e^8r
125 = A * e^11r
Divide:
=> 125/ 125 = e^ -3r
Take ln:
=> - 3r = ln125/ 175
=> r = .112 = 11.2 %
Thus A = 125/ e^11r = 125/3.43 = $36.4