Approximately 5,000 bacteria are placed in a culture. Let P  ( t  ) be the number of bacteria present in the culture after t  hours, and suppose that P  ( t  ) satisfies the differential equation

P  ^'  ( t  ) = .55 P  ( t  ).

(a) Find the formula for P  ( t  ).
P  ( t  ) =


(b) What is P  (0)?
P  (0) =

(c) How many bacteria are there after 5 hours?
bacteria

(d) What is the growth constant?


(e) Use the differential equation to determine how fast the bacteria culture is growing when it reaches 50,000.
bacteria per hour

(f) What is the size of the bacteria culture when it is growing at the rate of 24,000 bacteria per hour?
bacteria