A vat contains 500 gallons of 4% alcohol (by volume). Beer with 7% alcohol is pumped into the tank at a rate of 5 gallons per minute. Beer is also pumped out of the vat at a rate of 5 gallons per minute, so there is always 500 gallons in the tank. Set up an initial value problem to model the percentage of alcohol in the vat at time \(t\text{,}\) where \(t\) is the elapsed time in minutes.