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Mth163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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SR depth deviation question
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The above model was based on three data points. Suppose that other data points included (20,63) and (50,27). We do not expect that these points will necessarily fit the model exactly, since the model was obtained from the original three points. We can check to see how close (20,63) is to the model by substituting t = 20 to see how close our result is to 63. Check for yourself that when t = 20, we obtain depth = 64, which differs from the observed depth of 63. The observed depth differs from a model by -1, since 63 is one unit less than 64. You should check that the other data point (50,27) differs from the model by +2.
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How did you know that the next two points would differ from the observation by +2 without plugging the points into the equation??? Is it due to the time change from 20 to 50??? Is it knowing that the interval would increase at time intervals of 10, where 30 would be 0, 40 at +1 and therefor 50 would have to be +2???
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This could have been determined using the differential, which is a calculus technique you wouldn't be expected at the precalculus level to understand.
Or I could have just calculated it in advance.
From your point of view, at this point there isn't a good way to predict the deviation. The question simply asked you to verify, as part of the process of showing you what a deviation is.
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