42. Insect Growth The growth of a population of rare South American beetles is given by the logistic function with * = 0.00001 and t in months. Assume that there are 200 beetles initially and that the maximum population size is 10,000. a. Find the growth function G(t) for these beetles. Find the population and rate of growth of the population after the following times. b. 6 months c. 3 years d. 7 years e. What happens to the rate of growth over time?6. Disease Another disease hits the chronically ill town of Col- lege Station, Texas. This time the percent of the population in- fected by the disease t days after it hits town is approximated by p(t) = 10te-18 for 0 S t s 40. a. After how many days is the percent of the population in- fected a maximum? b. What is the maximum percent of the population infected?14. Birds The energy cost of bird flight as a function of body mass is given by E = 429m-0.35 where m is the mass of the bird (in grams) and E is the energy expenditure (in calories per gram per hour). Suppose that the mass of a 10-g bird is increasing at a rate of 0.001 g per hour. Find the rate at which the energy expenditure is changing with respect to time. Source: Wildlife Feeding and Nutrition