SOLUTION: The average SAT mathematics scores of incoming students at an eastern liberal arts college have been declining in recent years. In 2006, the average SAT score was 590; in 2012, it

Question 1047245: The average SAT mathematics scores of incoming students at an eastern liberal arts college have been declining in recent years. In 2006, the average SAT score was 590; in 2012, it was 560. Assuming the average SAT score varies linearly with time, answer these questions.
(a) Express the average SAT score in terms of time measured from 2006. (Use the following as necessary: S for the average SAT score and t for the time measured from 2006.)
(b) If the trend continues, what will the average SAT score of incoming students be in 2024?
(c) When will the average SAT score be 490?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The average SAT mathematics scores of incoming students at an eastern liberal arts college have been declining in recent years.
In 2006, the average SAT score was 590; in 2012, it was 560.
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Assuming the average SAT score varies linearly with time, answer these questions.
(a) Express the average SAT score in terms of time measured from 2006. (Use the following as necessary: S for the average SAT score and t for the time measured from 2006.)
Ans: (560-590)/6 = -5 per year
S(t) = 590-5t
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(b) If the trend continues, what will the average SAT score of incoming students be in 2024?
t = 18
S(18) = 590-5*18 = 590-90 = 500
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(c) When will the average SAT score be 490?
Solve for "t";;
490 = 590-5t
-100 = -5t
t = 20 years
Ans: 2006 + 20 years = 2026
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Cheers,
Stan H.
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