Your description corresponds to an exponential function.
So it is of the kind f(x) = A (e^kx)
Given that the pair (0,1) is in the graph, you can determine that A = 1:
1 = A (e ^ k*0)
=> 1 = A e^0
=> 1 = A
So, the function is of the kind f(x) = e^ (kx).
Where x is any positive value.
With that you can choose the right answer among your options.