The water tank shown above has a leak in the bottom. The tank will be empty in t=10 minutes. Answer the following questions about this leaky tank.
1. Do you expect the water level to be falling faster at t=4 or t=8 or will it drain at a constant rate? Why do you think this is so?
2. Let h(t) be the depth of the tank (in feet) at time t (in minutes). Sketch the graph of h(t) on the graph paper provided (you can do so by plugging values in to the applet).
3. Sketch the tangent line on your graph at t=4.
(a) Estimate the slope of this tangent line.
(b) What is the meaning of this number in the context of this problem? (Hint: what are the units?)
4. Repeat (3) for t=8.
5. Do (3) and (4) support your guess in (1)? Explain.
6. Estimate the (instantaneous) rate at which the water level is dropping at time t=4 by plugging values into the applet above. Your answer should be accurate to 1 decimal place.
7. Compare your answer to (6) with your answer to (3). (How should they compare?)