Excel does regressions. Do you have Excel?.
Let t=0 be 1965
A quadratic regression works pretty well.
Year Average Poverty Threshold (in $)
A.) Find a model for this data
B.) Estimate the average poverty threshold for a family of four in 1990
C.) Give a reasonable Domain and Range
Of course, the long way would be the algebraic, paper, pencil way.
I used a TI-84+ calculator to plot the data. I observed the data seemed to follow a parabolic curve. I performed a quadratic regression analysis to find the best quadratic equation that would best fit the curve. The equation I produced had a coefficient of determination of .9964. The closer this number is to 1, the better. This means the curve produced by my equation is pretty accurate.