1. One important issue in environmental health is being able to maintain air quality in workplaces. It has been been shown that extended exposure to carbon monoxide as low as 0.00012 can be harmful.

a. Consider a room with a volume of 1200 m³ containing machinery that produces carbon monoxide (CO) at a rate Q(t) = 0.0043 m³/hr. Assume that ventillation introduces fresh air at a rate f = 10 m³/hr. If c(t) is the concentration of CO in the room at any time, then the differential equation describing this situation is given by

If the room is initially free of CO, so c(0) = 0, then solve this differential equation. Graph the solution for 48 hours. Find how long it takes until the air becomes unhealthy (exceeds 0.00012). Eventually (limit as t tends to infinity), what will be the level of CO in this room?

b. The equilibrium concentration in the room is found by setting the right hand side of the differential equation equal to zero. Assuming that Q(t) and V are fixed at the levels in Part a., then find the minimum flow rate of fresh air f such that the equilibrium concentration is 0.00012.

c. In this part we assume that the machinery is producing CO in a cyclical manner with

Use the same flow rate f and volume V from Part a., then solve the new differential equation (with c(0) = 0) using the Improved Euler's method with h = 1 and t in the interval [0,200]. Graph the solution. From the output of the Improved Euler's method, find the first time when the air quality exceeds safe levels.