Final answer:
The average rate of change in gallons per minute does not necessarily change when the size of the tank is doubled, as the flow rate depends on multiple factors which may not be affected by the size of the tank alone.
Step-by-step explanation:
If the size of the tank referred to in question 5 is doubled, the average rate of change in gallons per minute does not necessarily change. The rate at which fluid flows out of a tank or through a tube is dependent on a number of factors including the pressure difference driving the flow, the viscosity of the fluid, the length and radius of the tube, and the gravitational force when dealing with tanks open to air. A key concept here is the continuity equation which states that, for an incompressible fluid, the volume flow rate must remain constant throughout the tube or tank. Therefore, solely increasing the size of the tank does not change the rate at which fluid leaves the tank if all other factors, such as the size of the hole and the height of the water above the hole, remain constant. However, if changing the size of the tank leads to a change in any of these factors, then the flow rate could be affected.