After3hours the number of bacteria in a culture is observed to have doubled.

(a) Find an exponential model P(t) =P₀e^kt, k> 0 for the number of bacteria in the culture at timet. (Roundkto four decimal places. Assumetis measured in hours.)

P(t) =

(b) Find the number of bacteria present in the culture after5hours. (Round your answer to four decimal places.)

p(5)= ( ) . p₀

(c) Find the time that it takes the culture to grow to60times its initial size. (Round your answer to two decimal places.)

t= ________ hr