Question

How do you find the inverse of the exponential growth function?

f(x)=9.16(1.0054)^x


I know the inverse of an exponential is the log but the function is not in the exponential form and I am not sure how to find c

Answer 1

The inverse function of f(x) is ... f⁻¹(x) = log (x/9.16)/log (1.0054)

Explanation:

Starting equation... f(x) = 9.16(1.0054)ˣ

Visually rewritten... y = 9.16(1.0054)ˣ

Flipping x and y... x = 9.16(1.0054)ʸ

Isolating (1.0054)ʸ... x/9.16 = (1.0054)ʸ

Taking the log of both sides... log (x/9.16) = y log (1.0054)

Isolating y... log (x/9.16)/log (1.0054) = y

Solution... y = log (x/9.16)/log (1.0054)