Which equation represents an exponential function with an initial value of 500?
f(x) = 100(5)x
f(x) = 100(x)5
f(x) = 500(2)x
f(x) = 500(x)2

The answer is third option. First thing: exponential functions have shape: c^x where c is some number. that means that second and forth option cannot be answer.

Second thing: we can also write exp functions as a*(c^x). for x=0, c^x = 1 which lets us with a*1 = a
Third option has a =500 which is why that is the answer.