Assume that Lake Erie has a volume of Vo in units km and that its rate of inflow (from Lake Huron) and outflow (to Lake Ontario) are both a constant value of r, in units km per year. Let y(t) denote the amount of pollutant at time t in Lake Erie. caused by (a) Suppose that at the time t = 0 (years), the pollutant concentration at Lake Erie past industrial pollution that has now been ordered to cease - is five times that of Lake Huron. Express the initial condition for y(t) in terms of Vo and , the pollutant concentration at Lake Huron which we assume to be constant. (b) Write the ODE that models the rate of change in pollution with respect to time at Lake Erie. The ODE should be in terms of y, r, Vo and H. (c) Solve the ODE from part (b) and use initial condition from part (a) to get the actual solution y(t) in terms of r, Vo and CH. (d) How long will it take to reduce the pollution concentration in Lake Erie to twice that of Lake Huron? Take Vo 480 km and r = 350 km. = (e) Suppose we are also interested in modeling the amount of pollution at Lake Ontario, denoted by z(t). Assuming that the volume of the lake stays constant, say at a value of V, write the ODE that models the rate of change in pollution at Lake Ontario with respect to time in terms of z, r, Vo, V, CH. Hint: You should be using your work from the previous parts since Lake Erie feeds into Lake Ontario.