Question 3

Shown in the figure below is lake Erie and lake Ontario and the main rivers flowing through them (the

arrows). Google says that the volume of lake Erie is about 500 km³ and lake Ontario is about

1500 km³ and the amount of water flowing through the lakes is about 60 km³ per year. Yes, that's

kilometers cubed. The goal is to model the amount of pollution in the two lakes at time t (years). We

will assume that initially, there is no pollution in either lake and that the river flowing into lake Erie is

polluted and is bringing in 30 tons of pollutant per year.

Let Er (t) be the amount of pollutant (in tons) in lake Erie at time t and let On (t) be the amount of

_pollutant (in tons) in lake Ontario at time t (years).

Part (a) Set up two differential equations, one for the amount of pollution in lake Erie at time t and the

other for the amount of pollution in lake Ontario at time t. This problem is very much like the tank

problem in the last assignment, except that here we have two tanks (two lakes).

Parb (b) Solve the differential equations and plot the solutions for a suitable time domain. You

should see that the amount of pollutant in each lake increases from 0 to a maximum. What are the

_maximums?

Part (c) Using the DEplot command in the DEtools package, generate a field plot with solution curves

for initial values Er (0) = 0, On (0) = 0 and Er(0) = 500, On (0) = 0 and

Er (0) = 500, On(0) = 1500 on the same plot.