The logistic model often is used to model the initial growth phase of a cancerous tumour or human population growth when resources are limited. The logistic model also plays a role in chemistry; it describes the concentrations of reactants and products in autocatalytic reactions. A constant carrying capacity, K. puts a "cap" on the growth of the population. The logistic growth equation is given by dN dt rN FN (1-A). N(0) = No where N(t) is the population size at time t, r> 0 is the per-capita growth rate. K is a constant carrying capacity, and No is the initial population size at t=0. a) Separate the variables and show that In N In K-N-rt+C. K where CER is the constant of integration. (Hint: Use partial fractions on b) Use laws of logarithms and show that you obtain a solution of the form N(K N) where C0 N K-N = Ce