Question 6

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Water is pumped into an underground tank at a constant rate of 8 gallons per minute. Water leaks out of the tank at the rate of  gallons per minute, for 0 ≤ t ≤ 120 minutes. At time t = 0, the tank contains 30 gallons of water.

(a) How many gallons of water leak out of the tank from time t = 0 to t = 3 minutes?

(b) How many gallons of water are in the tank at time t = 3 minutes?

(c) Write an expression for A(t), the total amount of water in the tank at time t.

(d) At what time t, 0 ≤ t ≤ 120, is the amount of water in the tank a maximum? Justify your answer.

Solution

I hereby claim this in the name of GreyM! Who ever wants to edit it just email me, sure all you know my email and I'll send you the file. (PS I've been trying to toy with the HTML to make this larger but it doesn't seem to be working for me, so if this appears massive for you, then well it worked...)

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