The logistic equation models the growth of a population. P(t) _ 5400 1 + 53e'*65t (a) Use the equation to find the value of k. k = (b) Use the equation to find the carrying capacity. (c) Use the equation to find the initial population. (d) Use the equation to determine when the population will reach 50% of its carrying capacity. (Round your answer to four decimal places.) yr (e) Use the equation to write a logistic differential equation that has the solution P(t). dP_ _