The logistic function defined by: 1 a + e-t N(t) = t0 represents the growth of a population. We will derive this func- tion by solving a differential equation model sume that a is a positive constant. As- (a) Determine where N(t) is increasing and where it is decreas- ing. (b) Find and classify any local extrema that the function has. (c) Where is the function concave up and where is it concave down? Find all inflection points of N(t). (d) Find lim; N(t) and decide whether N(t) has a horizontal asymptote. (e) Sketch the graph of N(t) together with its asymptotes and inflection points (if they exist). (f) Describe in words how the graph of the function changes if a is increased.