1. We have a large tank initially containing 1, 200 gallons of pure water. We begin adding an ethanol-water mix at a rate of 5 gallons per minute. This ethanol-water mix being added is 70 percent...

Extracted text: 1. We have a large tank initially containing 1, 200 gallons of pure water. We begin adding an ethanol-water mix at a rate of 5 gallons per minute. This ethanol-water mix being added is 70 percent ethanol. At the same time, the mixture in the tank is drained at a rate of 5 gallons per minute. Throughout this entire process, the mixture in the tank is thoroughly and uniformly mixed. Let y(t) be the number of gallons of pure ethanol in the tank t minutes after we started adding the ethanol-water mix. (a) Find the differential equation which describes this scenario (for y(t)). You must explain in your own words and logically derive the equation. (b) Using the differential equation just obtained, solve for y(t). (c) Approximately how many gallons of ethanol are in the tank at i. t = 30? ii. t = 70? iii. t = 1200? (d) When will the mixture in the tank be 75% ethanol?