Problem 4.2 ( Textbook: Figure 2.5 on P84): Hypothetically, a patient is diagnosed to have Po coronavirus at time t = 0 and these viruses grow subsequently (nobody really knows the truth but we assume) according to = -aP(M – P) where P(t) is the number of the cells at time t while a and M are two given positive constants. The patient will die when the number of bugs approaches infinity. Consider the case Po > M, find the time the patient has left to live, timed from t = 0. Your result is a formula with the given parameters Pg, M, a. For a more concrete example, please set P, = 1984, M = 1000, a = 1. Compute the patient's survival time. dP Never mind if the number is small when you use, a = 1 as no unit is given. If you insist having a "reasonable" number, I set a = 10 for which the time unit is week. Either number you use is correct for your HW solution.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.