course Mth 173
Rate of Depth Change is: y?t) = 2a(t) + b
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y?t) = 2(.193)(t) + -2.1
y?t) = .386(t) + -2.1
y?13.9) = .386(13.9) + -2.1
y?13.9) = 5.3654 + -2.1
= 3.2654
y?t) = 2a(t) + b
y?t) = 2(.193)(t) + -2.1
y?t) = .386(t) + -2.1
y?27.8) = .386(27.8) + -2.1
y?27.8) = 10.7308 + -2.1
= 8.6308
3.2654 - 8.6308 = -5.3654 (depth change)
** 3.2654 and 8.6308 are not depths, so their difference is not depth change.
What does y ' (t) represent?
*(*( It represents the rate at which depth is changing.
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What therefore do 3.2654 and 8.6308 represent? **
*(*( How fast/slow(rates) the depth is changing.
y(13.9) = 3.2654
y(27.8) = 8.6308
3.2654 + 8.6308 = 11.8962
11.8962/13.9 = .8558 (average rate of depth change)
The rate of depth change varies from about 3.3 to about 8.6. Over this interval the rate of depth change is constantly increasing from the lower to the higher value. So the average value of the rate of depth change would not be .856. This would be much like saying that your speedometer goes steadily upward from 20 mph to 60 mph, and your average speed is 2 mph.
If your speed went steadily from 20 mph to 60 mph, what would be the avearage speed?
If your rate of depth change goes from 3.3 to 8.6, what is the average rate of depth change?
Once you know the average rate of depth change for this interval, what can you then find? Hint: What is the definition of the average rate of change of depth with respect to clock time?
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