SOLUTION: SAT scores One small college has observed a downward trend in the average SAT score of applicants to the college. Analysis has resulted to the equation.

Question 800472: SAT scores One small college has observed a downward trend in the average SAT score of applicants to the college. Analysis has resulted to the equation.
s=620 - 4.5t
where s equals to average SAT score for a given year t equals time measured in year since 1985(t=0).
(a) Identify the t and s intercept
(b) Interpret the meaning of the intercepts. (Does your interpretation of the t intercept make sense)
(c) Interpret the meaning of slope.
(d) Sketch the equation.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

= average SAT score for a given year
= time measured in years since 1985 (t=0).

(a) The s intercept is , the s value when t=0.
The t-intercept is the t value for , and is tthe solution to the equation

Solving:

as an exact value, but the approximation would make a little more sense.

(b) The meaning of the s-intercept is clear and makes sense. It is just the average SAT score for the year 1985, which was taken as .
The t-intercept is an extrapolation that does not make much sense.
It means that if the trend continued the average would reach zero in the year .
It does not make sense to extrapolate to a trend detected over a short range of values.
The t range analyzed (time since 1985) cannot have been more than 2013-1985=28 years.
It does not make sense to project a trend that far into the future.
If we try to get more realistic, SAT scores were "re-centered" in the mid or late 1990's, and could be "re-centered" again in the next 110 years, so I would not take the current trend too seriously.

(c) The slope of the trend line is and can be interpreted as meaning that the average SAT score has been decreasing by points per year.
If we want to read more into the meaning of the slope, we could say that it illustrates the decline of education in the US.
Or maybe we could say that as a larger percentage of high school students take the SAT from year to year, and/or apply to that college, the percentage of poorly prepared, low-scoring SAT takers has been increasing and driving down the average.
Maybe the college as been attracting more and more low-scorers by doing too good a job of presenting itself as welcoming all students, and not being a "selective" institution.

(d) Sketch the equation.

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