Question 20 (3 points) The flu is considered dangerous when the number of people getting sick is growing at a rate proportional to the number of people infected. Public health workers track flu infection rates and notice that the number of cases is doubling every day. Let F(t) be the number of people infected by the flu, where t is measured in days. Use differential equations to find the general solution to for F(t), where F(0) = 2 is the initial population. Question 21 (3 points) Bob heats up a bottle of milk for his baby, Jill, every morning. Jill will only drink the bottle if it is at 98 degrees. 30 Bob places the bottle in a cup of hot water (170 degrees). The bottle starts off at 35 degrees. After 2 minutes the bottle is 80 degrees. Use Newton's heating-cooling law, that the rate of change in the temperature, H, is proportional to the difference between the object and the surrounding temperature, to determine how long Bob should leave the bottle in the hot water. Assume that the water stays at 170 degrees. Question 22 (3 points) If a population of is becoming extinct and the population is decaying exponentially. Assume that there are 2,000 animals, and there will only be one animal in 50 years. What is k, the rate of decay