randomized problem

If the function y = .015 t2 + -1.7 t + 93 represents depth y vs. clock time t, then what is the average rate of depth change between clock time t = 13.9 and clock time t = 27.8?

1. .015 * (13.9)^2 + -1.7 (13.9) + 93= 72.27

2. .015 * (27.8)^2 + -1.7 (27.8) + 93=57.33

What is the rate of depth change at the clock time halfway between t = 13.9 and t = 27.8?

3. t= (13.9+27.8)/2= 20.85; .015 * (20.85)^2 + -1.7 (20.85) + 93=64.08

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y(t) is the depth function. The rate of depth change function is y '(t), not y(t). The rate function can also be called r(t).

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The depth function is of the form y = a t^2 + b t + c. The rate function is therefore y ' (t) = 2 a t + b.

Can you correct your rate function and modify your results? &#

What function represents the rate r of depth change at clock time t?

4. y= .015 t^2 + -1.7 t + 93

What is the clock time halfway between t = 13.9 and t = 27.8, and what is the rate of depth change at this instant?

5. 20.85; the rate of depth change is 64.08

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You have to plug the halfway clock time into the rate-of-change function. What is the rate-of-depth-change function for this depth function?

If the function r(t) = .193 t + -2.1 represents the rate at which depth is changing at clock time t, then how much depth change will there be between clock times t = 13.9 and t = 27.8?

6. .193 (27.8-13.9) + -2.1=.5827

?What function represents the depth?

7. r(T)= .193 t +-2.1

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The rate function is of the form y ' = m t + b, so the depth function will be a quadratic function y = .5 m t^2 + b t + c, where c can be any number that fits the problem.

?What would this function be if it was known that at clock time t = 0 the depth is 130 ?