K Line Model Trains
Question Calculus, Differential Equations Year Uni first.?
(1 point) Let P (t) the performance level of someone who is learning a ability in terms of training time t. The derivative dP / dt represents the rate at which performance improves. If M is the maximum level of performance which the student is able, then a learning model is given by the differential equation dP / dt = k (MP (t)) where k is a positive constant. Two new workers Jim and John, were hired for an assembly line. Jim could process 11 units per minute after one hour and 14 units per minute after two hours. John could process 10 units per minute after one hour and 15 units per minute after two hours. Using the above example and assuming that P (0) estimated = 0, the maximum number units per minute for each worker is capable of processing. Jim:? John:?
Reorganize and integrate both sides to get:-In | MP (t) | = kt + C, where M = / = P (t) and C is a real number. Reorganize for P (t): P (t) = M-1 / (Ae ^ (kt)), where A = / = 0. A subbing solved by P (0) = 0: A = 1 / M therefore P (t) = GM / e ^ (kt) to find M for each person, use the given points. For Jim, the points are (1.11) and (2, 14). Start with (1.11) 11 = MM / k ^ and Reorganization for k, we obtain k = ln (1.11 / M) … For equation 1 (2, 14) you'll find that k = ln (1-14 / M) / 2 … the That Equation 2 Equation 1 = Equation 2. Ln (1-11 / m) = Ln (1-14 / M) / 2 2LN (1-11 / m) = Ln (1-14 / M) Ln (1-11 / M) ^ 2 = Ln (1 -14 / M) -> Raise both sides to e. (1-11 / m) ^ 2 = 14.1 / m -> now to resolve MM = 121 / 8 for John, you will experience the same process, ending with M = 20
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