Linear approximation Median home prices in Austin

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Linear approximationMedian home prices in Austin
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Tangent lines often give better linear
approximations than secant lines
tangent line approximation at 1996
secant line approximation 1995 to 1996
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Recall that we defined M'(t) by averaging the two
adjacent secant lines at each data point
For the endpoints 1994 and 2002, there is only
one interval to use so no average is taken
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Use both linear methods to estimate the
population in 1997
Secant line method (the old way)
Actual value 112,200
Tangent line method (the new way)
Average of secant slopes from 1995 to 1996 and
from 1996 to 1997