The number of males per 100 females, age 70 or over, in the United States for some recent years is shown in the following table.

(a) Plot the data, letting t be the years since 1970.

(b) Would a linear or quadratic function best model these data? Explain.
(c) If your graphing calculator has a quadratic regression feature, find the quadratic function that best fits the data. Graph this function on the same calculator window as the data.
(d) Choose the lowest point in the table above as the vertex and (48, 76.08) as a second point to find a quadratic function defined by ƒ(t) = a(t - h)² + k that models the data.
(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?
(f) Estimate the number of males per 100 females in 2015 using the two functions from parts (c) and (d), and compare with the actual figure of 74.55.

Transcribed Image Text:

Year 1970 1980 1990 2000 2010 2018 Males per 100 Females 66.53 62.04 62.60 65.51 71.94 76.08