Set up an initial value differential equation to model the following situation. Make sure to show all work. Elon Musk, his business partner Jeff Bezos, and 100 other 100 are waiting for the new model Tesla to come out, consider this moment to be time t=0. Elon and his friends then go to an after party and watch the purchases being made at a rate that is jointly proportional to the number of people that have purchased a new Tesla(X) and the number of people who have not purchased the new model Tesla. (a) Use a proportionality constant of 0.02 and write the differential equation and initial condition that models the spread of vehicle purchases.
1. Set up an initial value differential equation to model the following situation. Make sure to show all work.
Elon Musk, his business partner Jeff Bezos, and 100 other 100 are waiting for the new model Tesla to come out, consider this moment to be time t=0. Elon and his friends then go to an after party and watch the purchases being made at a rate that is jointly proportional to the number of people that have purchased a new Tesla(X) and the number of people who have not purchased the new model Tesla.
(a) Use a proportionality constant of 0.02 and write the differential equation and initial condition that models the spread of vehicle purchases.
(b) Find the the critial points of the DE and sketch a phase graph for the solution function X(t).
(c) Using the initial condition and the phase graph, draw a possible sketch for the solution function of X(t) might look like.
e) Use the separation of variables to find the implicit solution to the Differential Equation.
Step by step
Solved in 2 steps
