Question

suppose that f is a function of the form f(x)=Ae^kx, f(1)=5 and f(2)=15. Find A and k.

Answer 1

plug in the given values of f(x) and x:-
f(1) = 5 means that f(x) is 5 when x = 1

Answer 2

so we have
5 = Ae^k and
15 = Ae^(2k)

Answer 3

now you can find A and k by solving the above system of equations