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course Mth 173
1/30/11 4:29 pm
If the function y = .029 t2 + -1.4 t + 88 represents depth y vs. clock time t, then what is the average rate of depth change between clock time t = 6.4 and clock time t = 12.8? What is the rate of depth change at the clock time halfway between t = 6.4 and t = 12.8?What function represents the rate (r) of depth change at clock time t? What is the clock time halfway between t = 6.4 and t = 12.8, and what is the rate of depth change at this instant?
If the function r(t) = .211 t + -1.8 represents the rate at which depth is changing at clock time t, then how much depth change will there be between clock times t = 6.4 and t = 12.8?
• What function represents the depth?
• What would this function be if it was known that at clock time t = 0 the depth is 80 ?
The average rate of change between clock time t=6.4 and t=12.8 is -0.8432 cm/sec. The average rate of change halfway between clock time t=6.4 and t=12.8 is -0.936 cm/sec.
The function y=0.029t^2 + -1.4t + 88 represents the rate of depth change at clock time. The clock time half way between t=6.4 and t=12.8 is t=9.6. The rate of depth change at t=9.6 is -0.936 cm/sec.
@& You don't show how you calculated these first two results.
However the function y=0.029t^2 + -1.4t + 88 does not represent the rate of change of the depth, it represents the depth itself.*@
For the function r(t)= 0.211t + -1.8, if t=6.4, then r= -0.4496. If t=12.8, then r=0.9008. R(t)=0.211t + -1.8 represents the rate at which depth is changing. If clock time was t=0 and depth is 80, the function would be y= 0t + 80 (I am not sure how to do the last problem about clock time t=0 and depth =80. I see it as only one point, so there is no slope, and the y-intercept is 80, and that is how I got the function for the last answer).
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@& You are given the rate function. You need to find the depth function.
If the depth function is y = a t^2 + b t + c, then the rate function is r = 2 a t + b. You have to use this information to deduce the depth function from the given rate function.*@
@& Give this question another try.
Explain the details you used for the first two questions.
See if you can find the y = a t^2 + b t + c depth function for the given rate function.
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