Help with inverse function conceptual question?

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?

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Answer 1 · 2017-11-12T11:31:36

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

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.