7. For logistic modeling of an animal population in a limited environment situation, we have data for the birth rate, Bo = 0.1 month ; the death rate, So = 0.05 month, and a population- dependent, decreasing birth rate function that is proportional to the population size according to B = 0.0001 (animals * month)-. What is the time-dependent differential equation for this population? What is the value of the critical point for this population? Show that this critical point is stable. If the initial population is Po = 200 animals, how many months does it take for this population to grow by 200 more animals? If the initial population is Po= 800 animals, can we expect this population to grow by 200 more animals? If yes, how long will it take? If no, then explain why not.