the number of cells in a culture after x hours is given by the function y(x)=1.3e^(4x) How many hours must we wait until 6 million cells are in a culture inverse function

Question

The number of cells in a culture after x hours is given by the function y(x)=1.3e^(4x).Create the inverse function that perdicts the number of cells are in a culture.  How many hours must we wait until 6 million cells are in a culture.

Answer 1

6000000=y(x)=1.3e⁴ˣ. Inverse function: x=¼ln(y/1.3) or y(x)=¼ln(x/1.3), where y is the time in hours for x cells to cultivate in the culture.

ln(6000000)=ln(1.3)+4x.

4x=15.3450, x=3.8362 hrs approx.