Answer:
f(x)=4(2)^x-1, or f(1)=4,f(x)=f(x-1)(2)
Explanation:
The first equation above is the Explicit Geometric Formula, while the equation on the right is the Recursive Geometric Formula. This is how you find both.
Explicit Geometric Formula:
The formula for this is f(x)=a(r)^x-1, a being the first term, and r being the common ratio.
A, our starting term, or first term, is x = 1, and the term is 4, since that is the corresponding y to x = 1.
Our common ratio is 2, because as x increases by 1, y doubles.
Recursive Geometric Formula:
The formula for this is f(1)=a,f(x)=f(x-1)(r), a being the first term, and r being the common ratio.
As said above, A is 4, and r is 2.
Plug it in and you get f(1)=4,f(x)=f(x-1)(2)