Problem 54735. Solve an ODE: concentrations predicted by the cells-in-series model

One approach for predicting mixing and transport of contaminants in a river is the cells-in-series model. The model divides a river into several well-mixed cells of volume V. Then if the discharge (i.e., the volume of water flowing past a cross section per unit time) is Q and the first-order decay coefficient (dimensions of time^{-1}) is k, the concentration C_n in the nth cell is given by
V dC_n/dt = Q C_{n-1} - Q C_n - kVC_n
Write a function to compute the maximum concentration in the nth cell and the time it occurs assuming that the concentration in the first cell (i.e., n = 1) is C_in at time t = 0 and no contaminant enters the first cell from upstream.

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100.0% Correct | 0.0% Incorrect
Last Solution submitted on Jun 24, 2022

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