A certain bacteria grows according to the function P$.$ Consider P a solution to the logistic differential equation dP over dt equals $3$ times P times quantity $4$ minus P over $7000$ end quantity comma where P is the population of bacteria and t is measured in days.Part A: If P$(0)=2,400,$ solve for P$($t$).(10$ points$)$Part B: What is the largest rate of increase in the number of bacteria? $(10$ points$)$Part C: What will be the maximum number of bacteria? Explain your reasoning. $(10$ points$)$