A local swimming pool in Gilbert needs to be treated for the summer. Arizona Gills has a pool that houses 135,000 gallons of water. Chlorine concentration in a pool is often measured in parts per million (ppm). The pool currently has 6,000 gallons of water and a very low chlorine concentration of 0.2 ppm. This is too low to be safe and sanitary. The Center for Disease Control and Prevention (CDC) requires public pools to have a chlorine concentration of 3 parts per million in order to operate. In more practical terms, 13 fl. oz. of chlorine must be added to raise the chlorine concentration a 10,000 gallon body of water by 1 ppm. You can also assume there are 13 fl. oz. of chlorine in a 10,000 gallon body of water that has a chlorine concentration of 1.0 ppm. We assume the chlorine is always well-mixed when it enters the pool. Water will be pumped into the pool at a rate of 10,000 gallons per hour with a currently unknown concentration of chlorine. Water will not be pumped out, as that would work against the goals of getting the pool opened to the public. Arizona Gills opens in 12 hours.

1. Write a differential equation for , the number of fluid ounces of chlorine in the pool at time hours since workers began filling up the pool from the initial 5,000 gallons.

2. Solve the ODE using the appropriate method.