(a) A kitchen sink has a volume of 15 L. If the drain is closed and the sink is initially empty, plot the volume of water in the sink as a function of time. How long will it take to overflow the sink after the faucet is open, allowing a flow rate of 0.3 L/min? (b) Re-answer the previous problem, but assume that the drain is partially opened 10 minutes after the water flow starts, allowing water to flow out at a constant rate of 0.1 L/min.

The relationship between the volume, V, measured in cm³, of a balloon and the internal air pressure, P, measured in grams/cm², is given by PV = 45 000. The volume of a balloon is increasing at a rate of 100 cm³s-1. Find the rate of change of the air pressure inside the balloon when the volume is 4 000 cm³.

When drugs are administered into the bloodstream, the amount of the drug present decreases continuously at a constant rate. The amount of a certain drug, Xanaz, in the bloodstream is modeled by the function, where is the initial dosage, and t is the time (in hours) after the initial dose was given. The following chart shows the relationship between the original dose and how much is sti in the system after so much time. Xanax (3mg) amount still in system after X hours 2.5 1.5 0.5 2 10 12 14 16 18 20 22 24 Number of hours after dose was taken After how many hours will there be approximately 1/2 of the original dose in the body? 3. 2. 1. Amount still in the system in mg's