Linear approximation Median home prices in Austin

Tangent lines often give better linear approximations than secant lines secant line approximation 1995 to 1996 tangent line approximation at 1996

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

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