Question

F a tank holds 6000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli's law gives the volume of water remaining in the tank after t minutes as V(t) = 6000(1 - (t/40)). Find the rate at which the water is draining out of the tank after:

a) 5 minutes
b) 7 minutes
c) 9 minutes
d) 12 minutes

Answer 1

The rate at which the water is draining out of the tank after 5, 7, 9, and 12 minutes is -150 gallons per minute for each of these time points, as it is derived from the constant rate of change given by the derivative of the volume function.

Step-by-step explanation:

The volume of water remaining in the tank after t minutes is given by the formula V(t) = 6000(1 - (t/40)). To find the rate at which the water is draining out of the tank, we need to take the derivative of V(t) with respect to time t. The derivative V'(t) will tell us the rate of change of volume, which is the rate at which the water is draining from the tank.

The derivative is V'(t) = -6000/40 = -150. This signifies that water drains from the tank at a rate of 150 gallons per minute at any point in time during the drainage, which is a constant rate.

• The rate after 5 minutes is still -150 gallons per minute.
• The rate after 7 minutes is also -150 gallons per minute.
• The rate after 9 minutes remains -150 gallons per minute.
• Similarly, after 12 minutes, the drainage rate is still -150 gallons per minute.