Create the inverse function

Question

The number of cells in a culture after x hours is given by the function
y(x) = 7e^2x
Create the inverse function that predicts the number of hours we must wait until a given
number of cells are in that culture. How many hours must we wait until 1.8 million cells are in
the culture?

Answer 1

x = 7e^2y

x/7 = e^2y

ln(x/7) = 2y

ln(x/7)/2 = y

f^-1(x) = ln(x/7)/2

Plug in 1.8 million for x for your answer.