Help with inverse function conceptual question?

Let P = 25 ln(t) give the annual profit of a company (in thousands of dollars) t years after its formation. What is P^-1(37) and what does this value represent? Round to the nearest whole number and include units.

I think the answer is
P^-1(37) is the number of years after 2025 at which there were $37,000 of annual profit.

Am I correct?

1 Answer
Nov 12, 2017

P^(-1)(37) is the number of years - approximately 4 - after formation at which there was $37,000 annual profit.

Explanation:

If P(t) = 25 ln(t) and P(t) = 37, then:

25 ln(t) = 37

So:

ln(t) = 37/25

and:

t = e^(37/25) ~~ 4.392 years after formation.

That is 4 years after formation rounded to the nearest year.