(a) The initial value of water in the tank is 88 gallons, and the rate of change is -6 gallons per minute (since the water is being drained). Therefore, the function that represents the amount of water in the tank, Y, after X minutes is: Y = -6X + 88.
(b) We know that the amount of water left in the tank is 34 gallons. To find out how long the tank has been draining for, we can plug in 34 for Y in the function and solve for X:
34 = -6X + 88
-6X = -54
X = 9
Therefore, the tank has been draining for 9 minutes.