Please answer each of the following questions. You should work them out on a separate sheet of paper and upload your work. Be sure to show all your work. Typed responses are not permitted without prior approval from your teacher. Calculators are permitted on this assignment. 1. Given that the acceleration of a particle is -21 ft/sec 2 and that its initial velocity and distance are 4 ft/sec and 14 ft, respectively. Determine the equations for a. Determine the equation for the velocity of the particle. b. Determine the equation for the position of the particle. 2. Assume that the growth rate of a population of ants is proportional to the size of the population at each instant of time. Suppose 100 ants are present initially and 230 are present after 3 days. a. Write a differential equation that models the population of the ants. b. Solve the differential equation with the initial conditions. c. What is the population of the ants after 14 days? 3. A detective discovers a corpse in an abandoned building, and nds that its temperature is 27 C. An hour later its temperature is 21 C. Assume that the temperature of the air in the building is 8, and normal body temperature is 37. Newton's Law of Cooling applies to the corpse. a. Write the differential equation which models the temperature of the body, H, as a function of time t, where t = 0 is the moment of death. b. Solve the differential equation. c. How long had the corpse been dead at the moment it was discovered