Fibonacci Series with Dynamic Programming
$n$ is the index of the Fibonacci number you're computing. For example, the sixth Fibonacci number, $f(6)$, is equal to 8.

If we assume that function calls take constant time and we are using your model, then it's clear that the number of calls, $C(n)$, to compute the $n$-th Fib will be given by 
$$C(n)=C(n-1)+C(n-2)$$
with $C(0)$ and $C(1)$ both being 1.

Hmm. That recurrence is almost exactly the recurrence for the Fibs, just shifted by a place, so we have $C(n)=f(n+1)$. In other words, the asymptotic growth of $C(n)$ is the same as the Fibs themselves.