A population of bacteria is modelled by the equation: P(t) = 2509.231: Where P(t) is the population of individuals, and t is the time measured in hours. A) What will the population of bacteria be after 4 hours? B) At what time will the population be equal to 1200 bacteria? C) Find an expression for the rate of change of the bacteria population. D) Find the rate of change of the bacteria population at t = 4 hours. E) Will the rate of change ever be negative? Briefly explain