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 t represent the 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?