The number of bacteria in a culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours.

a) Find the initial population.

b) Write an exponential growth model for the bacteria population. Let represent time in hours.

c) Use the model to determine the number of bacteria after 8 hours.

d) After how many hours will the bacteria count be 25,000?