The mean annual U.S. per-person consumptions of milk and soft drinks are shown in Table 17 for various years.

a. Let M(t) be the mean annual per-person consumption of milk and S(t) be the mean annual per-person consumption of soft drinks, both in gallons per person, in the year that is t years since 1900. Find linear equations of M and S.
b. Graph both models for the period 1970€“2005 on the same coordinate system.
c. Do the models estimate that the mean annual per-person consumption of milk was ever equal to the mean annual per- person consumption of soft drinks? If so, what is that mean annual per-person consumption, and when did it occur?
d. Do the models estimate that the mean annual per-person consumption of milk was ever greater than the mean annual per-person consumption of soft drinks? If so, in what years?

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Table 17 Mean Annual U.S Per-Person Consumptions of Milk and Soft Drinks Mean Annual Consumption of Milk Mean Annual Consumption of Soft Drinks Year gallons per person) Ye(gallons per person) 970 1980 1985 1990 1995 2000 2005 31.3 27.5 26.7 25.7 23.9 22,5 21.0 1950 1960 970 1980 1990 2000 2005 10.8 13.4 24.3 35.1 46.2 49.3 51.5