The depth of water in a certain uniform cylinder is given by the depth vs. clock time function y = .025 t² + -1.6 t + 51.  

What is the average rate at which depth changes between clock times t = 9 and t = 18?

• What is the clock time halfway between t = 9 and t = 18, and what is the rate of depth change at this instant?
• What function represents the rate r of depth change at clock time t?
• What is the value of this function at the clock time halfway between t = 9 and t = 18?

If the rate of depth change is given by dy/dt = .096 t + -2.1 then how much depth change will there be between clock times t = 9 and t = 18?

• Give the function that represents the depth.
• Give the specific function corresponding to depth 100 at clock time t = 0.