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1. A wl-mixed pond of constant volume V has a river flowing into it and a river flowing out of it, both at volumetric flow rate q. The ponds are initially (t 0) pristine (free of pollution). At time t = 0+1 however, pollution from a factory causes the incoming river to have a concentration c(t) of pollutant pel im on (a) Write a dynamic model for c(t), the concentration of pollutant in the pond at time t. Write the initial condition Because the pond is initially pristine, c is considered deviation from a pristine pond c, is considered deviation from pollution-free, and your model is already in deviation form. (b) Derive the transfer function G(s) relating the response of c(t) to incoming pollutant (c) Draw the block flow diagram for this very simple system and write the transfer (d) Consider the pollutant scheme: levels c,(t). Write it in gain-time constant form. function in the box. 0 t <0 Ci(t) p t20 where p is the sustained level of pollution in the river after time zero. Use the transfer function G(s) to determine the resulting pollutant concentration c(t) in the pond. Sketch the response c(t) and label the limiting value of c(t) astoo (e) On the same plot, sketch the response c(t) if the pond were smallen

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