A bacteria culture starts with 900 bacteria and grows at a rate proportional to its size. After 4 hours there will be 3600 bacteria.

(a) Express the population P after t hours as a function of t.
P(t)=


(b) What will be the population after 2 hours?

(c) How long will it take for the population to reach 2870? Give your answer accurate to at least 2 decimal places.