The following table gives the median age at their first marriage of women in the United States for some selected years.

a. Plot the data using x = 40 for 1940, and so on.

b.Would a linear or quadratic function best model this data? Explain.

c. If your graphing calculator has a regression feature, find the quadratic function that best fits the data. Graph this function on the same calculator window as the data. (On a TI-84 Plus calculator, press the STAT key, and then select the CALC menu. QuadReg is item 5. The command QuadReg L₁,L₂,Y₁ finds the quadratic regression equation for the data in L₁  and L₂ and stores the function in y₁.)

d. Find a quadratic function defined by f(x) = a(x – h)² + k that models the data using (60, 20.3) as the vertex and then choosing (100, 25.1) as a second point to determine the value of a.

e. Graph the function from part d on the same calculator window as the data and function from part c. Do the graphs of the two functions differ by much?

Transcribed Image Text:

Year 1940 1950 1960 1970 1980 1990 2000 Age 21.5 20.3 20.3 20.8 22.0 23.9 25.1