The depth of water in a certain uniform cylinder is given by the depth vs. clock time function y = .015 t² + -1.3 t + 90.  

What is the average rate at which depth changes between clock times t = 11.7 and t = 23.4?

• What is the clock time halfway between t = 11.7 and t = 23.4, 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 = 11.7 and t = 23.4?

If the rate of depth change is given by dy/dt = .29 t + -3 then how much depth change will there be between clock times t = 11.7 and t = 23.4?

• Give the function that represents the depth.
• Give the specific function corresponding to depth 70 at clock time t = 0.