(25 points) Consider a logistic population model with growth rate of 13yr-1 and carrying capacity of 100,000.a)Write the DE for this model and its solution. (You need not solve the DE, just write the solution as found in the class notes or the text.) Describe the qualitative behavior of the solutions.b) If there are initially 5000 organisms, how many will there be after 1 year? After 5 years? When will there be 50,000?c) Add to this model the effects of harvesting by assuming that a fraction qPqq$15,00010%q,0,of the population are removed each year. (i.e. The number of organisms harvested each year isqP, where Pis the population.) Write the new DE for this model and discuss the qualitative behavior of the population compared to the basic logistic model for various values of the emigration parameter q. What is the largest values ofq that allows the existence of a sustained population?3.(25 points)a