2 mark for review the rate at which water leaks from a tank, in gallons per hour, is modeled by r, a…

2 mark for review the rate at which water leaks from a tank, in gallons per hour, is modeled by r, a differentiable function of the number of hours after the leak is discovered. which of the following is the best interpretation of r(3)? a the amount of water, in gallons, that has leaked out of the tank during the first three hours after the leak is discovered b the amount of change, in gallons per hour, in the rate at which water is leaking during the three hours after the leak is discovered c the rate at which water leaks from the tank, in gallons per hour, three hours after the leak is discovered d the rate of change of the rate at which water leaks from the tank, in gallons per hour per hour, three hours after the leak is discovered

2 mark for review the rate at which water leaks from a tank, in gallons per hour, is modeled by r, a differentiable function of the number of hours after the leak is discovered. which of the following is the best interpretation of r(3)? a the amount of water, in gallons, that has leaked out of the tank during the first three hours after the leak is discovered b the amount of change, in gallons per hour, in the rate at which water is leaking during the three hours after the leak is discovered c the rate at which water leaks from the tank, in gallons per hour, three hours after the leak is discovered d the rate of change of the rate at which water leaks from the tank, in gallons per hour per hour, three hours after the leak is discovered

Answer

Brief Explanations:

The derivative of a function representing a rate - here the rate of water leakage $R(t)$ (where $t$ is the number of hours after the leak is discovered) gives the rate of change of that rate. $R'(3)$ is the derivative of the rate function $R(t)$ evaluated at $t = 3$. So it represents the rate of change of the rate at which water leaks from the tank, in gallons per hour per hour, three hours after the leak is discovered.

Answer:

D. The rate of change of the rate at which water leaks from the tank, in gallons per hour per hour, three hours after the leak is discovered