A population is modeled by a function P that satisfies the logistic differential equation dP/dt=P/2(3-P/20) where the initial population P(O)=100 and t is the time in years. (a) What is lim P(t) as t->infinity? (b) For what values of P is the population growing the fastest? (c) Find the slope of the graph of P at the point of inflection