Consider a population of a single species of bacteria in a petri dish, which has limited resources (in terms of space or nutrition). Suppose that when the population is relatively small, the growth rate is proportional to the population with a proportionality factor of 3 per unit time. There is also a carrying capacity of 24 micrograms of bacteria, and a constant rate 6 of harvesting, that is assume 6 micrograms of bacteria per unit time are removed from the dish. a) Write a differential equation of the form P′ = F(P), which models this situation, where P is the bacteria population in micrograms as function of time. P' = ?b) Find the equilibrium solutions. Equilibrium Population:c) For what values of P is the population increasing? (Use interval notation)Population is Increasing:d) For what values of P is the population decreasing (Use interval notation)Population is Decreasing: