The graph of an exponential function passes through $(1,-20)$ and $(2,-80)$. Find the exponential function that describes the graph.
Provide your answer below:
\[
f(x)=
\]

Step 1 ：The general form of an exponential function is \(f(x) = ab^x\). We can use the two points given to form a system of equations and solve for \(a\) and \(b\).

Step 2 ：From the point (1, -20), we get the equation \(f(1) = -20 = ab\).

Step 3 ：From the point (2, -80), we get the equation \(f(2) = -80 = ab^2\).

Step 4 ：We can solve this system of equations to find the values of \(a\) and \(b\).

Step 5 ：The solution to the system of equations is \(a = -5\) and \(b = 4\). Therefore, the exponential function that describes the graph is \(f(x) = -5 \cdot 4^x\).

Step 6 ：Final Answer: \(\boxed{f(x) = -5 \cdot 4^x}\)