4. A new, gigantic 24-inch Apple iPad is introduced initially (on the 1st day of Sept. 2026) to twenty lucky Apple aficionados (this is time t = 0). Assume that there are 1000 people total in the local Apple community and... (a) Set up a DE to determine the number of people x(t) who have bought the new, huge iPad at time t, if we assume that the rate at which the new device is sold is jointly proportional (use k for the proportionality constant) to the number of people who have bought the new iPad and those who have not bought it. (b) If k = 0.2, use a Bernoulli substitution to solve this as a linear equation. DE. Show all steps needed to integrate. All integration and algebra should be shown in detail to solve for the explicit solution.