Around 1840, the belgian mathematician-biologist p. f. verhulst was concerned with mathematical formulations for predicting the human populations of various countries. one of the equations he studied was dp = p(a - b), where a and b are positive constants. equation (1) came to be known as the logistic equation and its solution is called the logistic function. given the initial condition p(0) = po, po + a/b, show (derive) that the solution to the o. d.e (1) is a po p(t) = b po + 6 po + (a - b po)e-at a (hint: separation of variables and partial fractions, ple-b] = + p)