36- Let k = l and M = IUD, and assume the initial population is 1(0) 2 5 _ (a) Solve the differential equation %x% = x( 100 1) for 1 _ (b) Graph the population x(t) for U E t E 20. (c) When will the population be 2U? 50? 90? 100? (d) What is the population after a "long"I time? (Find the limit, as t becomes arbitrarily large, of x .] (e) Explain the shape of the graph in (a) in terms of a population of bacteria. (f) When is the growth rate largest? (Maximize ddt .] (g) What is the population when the growth rate is largest