When you simplify the right-hand side of Equation (1) using your new expression for the integral, and then factor out and divide by P_L(0)you’ll get the following nice expression for the ratio P_L(t)/P_L(0):

a. Suppose that for Lake Michigan the constant p is equal to 0.02. Use a graph of the ratio P_L(t)/P_L(0) to estimate how long it will take to reduce pollution to 50% of its current value. How does this compare with the time, assuming pollution-free inflow?

b. If the constant p has the value 0 for Lake Michigan, what does that tell you about the pollution level in the inflow? In this case, what happens to the ratio P_L(t)/P_L(0) over time?

Equation 1

PL(1) P(0) 1 k-p (ke-pt-pe-).