Question

A chemist has been tracking the amount of bacteria grown over a period of days(x). The chemist's data is shown in the table. What is the inverse function of the chemist's exponential function shown in the table?

Answer 1

Answer:
`f'(x)=log_(4)x`

Explanation:

Lets first identify the function using the given data.

Clearly we can see the trend in the data.

The value of the function
`f(x)` is
`4^(x)`

So,
`f(x)=4^(x)`

Now we find the inverse of the function.

Let
`f'(x)` be the inverse function.

Now substitute
`f'(x)` in the place of
`x` and
`x` in the place of
`f(x)` in the above equation.

So,
`x=4^(f'(x))`

Applying logarithm on both sides,

`ln(x)=f'(x)ln(4)`

`f'(x)=log_(4)x`