II. Applications/Analysis (Technology allowed, show all work!) 1. Suppose you are given the following differential equation: dP dt - = 3P2 - 66P + 171 a) Find the equilibrium solutions for this equation (4 points). b) Using the 2"d derivative, determine the value of P where there is a change in concavity; that is, a point of inflection (4 points). c) Sketch the solution curves for this differential equation having initial points (0, 0), (0, 5), (0, 17), and (0, 20), along with the equilibrium solutions already found (6 points).2. Suppose you are given . 0416, a repeating decimal. By viewing the repeating part of this decimal as an infinite geometric series, convert the decimal into a completely simplified fraction (5 points). 3. Set up, and solve, a 1" order differential equation for the following situation: The time rate of change of an alligator population P in a swamp is directly proportional to the square of P. The swamp contained 1 dozen alligators in 2008 and 2 dozen alligators in 2018. In what year will there be 4 dozen alligators in the swamp (6 points)