SOLUTION: School Lunch Program: In 1970, 22.4 million students participated in the national school lunch program. By 2000, this number increased to 27.2 million students. (a) Find the slope

Algebra ->  Linear-equations -> SOLUTION: School Lunch Program: In 1970, 22.4 million students participated in the national school lunch program. By 2000, this number increased to 27.2 million students. (a) Find the slope       Log On


   

Question 476446: School Lunch Program: In 1970, 22.4 million students participated in the national school lunch program. By 2000, this number increased to 27.2 million students. (a) Find the slope of the line passing through the points (1970, 22.4) and (2000, 27.2). (b) Interpret the slope as a rate of change. (c) If this tend continues, estimate the number of participants in 2005.
Answer by josmiceli(19441) About Me  (Show Source):
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Let +p%28t%29+ = The number of participants, p, during year t
Let +t+=+0+ for the year 1970
then +t+=+30+ for the year 2000
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The equation is
+p+=+m%2At+%2B+p%280%29+ ( p is in millions)
+p%280%29+ is the count of participants for 1970
+p%280%29+=+22.4+
The slope,m, is (change in p) / (change in t)
+m+=+%28+27.2+-22.4+%29+%2F+%28+30+-+0+%29+
+m+=+4.8+%2F+30+
+m+=+.16+
The equation is:
+p+=+.16t+%2B+22.4+
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In 2005:
+p+=+.16%2A35+%2B+22.4+
+p+=+5.6+%2B+22.4+
+p+=+28+
The estimate for 2005 is 28 million students