1.) (Sections 4.1 & 4.2) A virus is spreading through a population, with 8% more people actively infected every 10 days. Initially there were 102 people actively infected. (a) Find an exponential model of the form V(t) = Abt that will compute the number of people actively infected V as a function of t in days. (b) What is the per-day rate of infection? Give as a percentage accurate to two decimal places (1.23% per day, for example). (c) What is the doubling time for infections? That is, how long until twice as many people are infected than initially? Give accurate to the nearest integer and label appropriately. 2.) (Sections 4.1 & 4.2) A city is looking to solve its homelessness problem over the next several years. Through a variety of interventions and programs, it wants to reduce the number of people experiencing homelessness by 15% every three years. (a) Find an exponential model of the form H(t) = Abt that computes the number of people experiencing homelessness in the city H as a function of t, years when the city's interventions and programs begin. (b) What is the per-year rate of decrease of homelessness in the city? Give as a percentage accurate to two decimal places (1.23% per year, for example). (c) Was is the half-life for homelessness in this city? That is, how long until half as many people are experiencing homelessness than initially? Give accurate to the nearest integer and label appropri- ately. 3.) (Sections 4.1 & 4.2) Expand log3 729(x + 5)2 y(z - 4)8 as much as possible. 4.) (Sections 4.3 & 4.4) Compute the equation of the line tangent to f(x) = 9r In(x2 - 4x + 5) - 5x2 when * = 2