Differential Equations: 1.) Set up an initial value problem to model the following situation. - You and 100 other people wait in a long line for the new model Tesla to come out, consider this to be time, t = 0. X will be represented by the number of people that have purchased a new model Tesla. a.) Write a differential equation, with a 0.02 constant and initial conditions that model the spread of Tesla's being purchased. b.)Find the critical points and sketch a phase graph for the function X(t). show all work c.) Next draw a sketch of what the solution would look like for X(t). d.) Show all work for the separation of variables to find the Implicit Solution.