The number y, in millions, of drug prescriptions filled by mail order in the united states from 1995 through 2008 can be modeled by y = 13.0t + 20 for 5 ≤ t ≤18 where t is the year with t = 5 corresponding to 1995.

a) according to the model, when did the number of prescriptions filled by mail order reach 100 million?

b) what is the slope of the model and what does it tell you about the number of prescriptions filled by mail in the united states?

c) do you think the model can be used to predict the number of prescriptions filled by mail order in the united states beyond 2008? if so, for what time period?

d) explain, both algebraically and graphically, how you could find the number of prescriptions filled by mail order reaches 300 million.

Y = 13t + 20; y in million

a.) the number of prescriptions filled by mail order will reach 100 million at y = 100
100 = 13t + 20
13t = 100 - 20 = 80
t = 80/13 = 6.15
Therefore, the number of prescriptions filled by mail order will reach 100 million in 1996

b.) The slope of the model is 13 and that means that each year the mail order fills 13 million new prescriptions.

c.) The model specified that 5 ≤ t ≤ 18 and t = 5 represent 1995, therefore, t = 18 will represent 2008. Therefore, the model cannot be used to predict the number of prescriptions filled by mail order beyond 2008.

d.) Algebraically,
300 = 13t + 20
13t = 300 - 20 = 280
t = 280/13 = 21.5
Therefore, the number of prescriptions filled by mail order will reach 300 million in 2011

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