Approximately 10,000 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 (t) = 0.55P(t). 

(a) What is P(0)? 

(b) Find the formula for P(t). 

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

(d) What is the growth constant? 

(e) Use the differential equation to determine how fast the bacteria culture is growing when it reaches 100,000. 

(f ) What is the size of the bacteria culture when it is growing at a rate of 34,000 bacteria per hour?