Suppose that instead of assuming that all pollution inflow immediately ceases, we model P_i(t) by a decaying exponential of the form a · e^–pt where p is a constant that tells us how fast the inflow is being cleaned of pollution. To simplify things, we’ll also assume that initially the inflow and the lake have the same pollution concentration, so a = P_L(0)Now substitute a = P_L(0)e^–px for P_i(x) in Equation (1), and evaluate the integral as a function of t.

Equation 1

Transcribed Image Text:

e-k[P₂(0) + k["P,(x)e²* dx] PL(t)= е (1)