You have a summer internship at the Ready Reservoir. Water enters the reservoir both from the Rapid River and from rainfall. The dam operators can control the flow of water out of the reservoir through the dam, in order to handle water needs for the town. As part of your internship, you spend ten days monitoring the volume of water in Ready Reservoir, starting at noon on July 1st. Reservoir water volume is often measured using units of thousands of acre-feet (kaf). One kaf is the amount of water that would cover 1 acre of land if the water were 1 ft deep, or roughly the amount of water in a medium-sized swimming pool.

The function r(t) is the rate, in kaf per day, at which water enters the reservoir t days after you start monitoring. This rate includes the water from both the Rapid River and rainfall.

The function s(t) is the rate, in kaf per day, at which water leaves the reservoir by flowing through the dam t days after you start monitoring.

You can assume that r(t) and s(t) give a complete description of all water entering and leaving the lake. When you start monitoring, there are 5,000 kaf of water in the reservoir. The graph below depicts r(t) as the solid black graph and s(t) as the red dashed graph. Notice that each segment of r(t) and of s(t) is linear.

12 11 10 of - - -- - - ---- 00 - - - -- - - -. OT - - - . CO 1 2 3 5 6 7 8 9 10 For each of the following subparts, represent the given statement with an expression involving r(t), s(t), their derivatives, and/or definite integrals. i. the amount of water (in kaf) which flows out through the dam between noon on July 8th and noon on July 10th ii. the rate at which water enters Ready Reservoir (in kaf per day) at 6pm on July 5th. iii. the total amount of water (in kaf) in Ready Reservoir at noon on July 4th for each of the following subparts, write a complete sentence giving a practical interpretation of the equation. . for (t ) - s(t ) dt = - 3 ii. 1 10 - 5 . s(t) dt = 4.3 In this part, you will determine when the Ready Reservoir has the least amount of water. i. Let W(t) represent the amount of water, in kaf, in the reservoir at time t. Write a formula for its derivative W'(t) in terms of r(t) and s(t). How can you visualize this on the graph above? ii. Find all times t which are local minima of W(t). iii. Find the time t which is the global minima of W(t). Note that you can do this without computing the exact values of W(t), but be sure to explain how you come up with any estimates