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4. Imagine you have a well-mixed lake with constant volume V [m³]. Water enters the lake from Stream A with a flow rate Q, and exits the lake from stream B at the same flow rate. The units of Q are m³/day. Assume the inlet stream contains two different microbes, microbe R and microbe S. The concentrations of these microbes in the inlet are Crin and Csin, respectively (units of g/m³). Let CR and Cs be the concentrations microbes in the lake (g/m³). = dt a) State the governing equation for CR CR and C = if the microbes grow logistically in the lake. Assume the growth rate parameters are r and r(units of 1/day), and the carrying capacities are KR and Ks (units of g). The carrying capacities represent the total mass of R and S than can be supported in the entire lake. For now, assume the two microbes do not interact with each other in any way. It is not necessary to solve the equations. b) Describe in words how you would determine the values of CR and Cs after a long time has passed. Assume you know the numerical value of all the parameters. c) Repeat part A, but this time assume that microbe R eats microbe S, such that the logistic growth of R depends on S, and S experiences predation. You can introduce new parameters as necessary, but please be sure to define the units. d) State how you would solve for the values of CR and Cs (for part C this time) after a long time has passed. Assume you know the numeric values of any parameters.