5) The number of people in a college dorm who get infected with a virus, over t days, grows according to the population with threshold model. A particular virus has a growth rate, k = 0.50, and a threshold of 120. a) Write the differential equation that describes the change, dt b) Draw the slope field using the software I used in the video or similar graphing software then paste it in this document where 0 ≤ t ≤ 10 and 0 ≤ P ≤ 150 c) Draw the equilibrium solution/s on the slope field. d) Draw the solution curve that passes through the point (0,50) e) What is lim P (what happens to the number of people who have caught the virus over time) 810