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student enrollment in a country's schools during a 16 year period is modeled by the equation n = -0.3|t-8|+11 where n is the number of students (in thousands) and t (in number of years since 1990)a. what was the enrollment since 1990? show how you found your answer b. in what year(s) was the enrollment closest to 10,000. Explain how to find the answer



Answer :

a. years since 1990 (t) = 30

enrollment: n = -0.3|30 - 8|+11 = -0.3*22 + 11 = 4.4, which means 4400 students

b. Replacing into the equation with n = 10, we get:

10 = -0.3|t - 8|+11

10 - 11 = -0.3|t - 8|

(-1)/(-0.3) = |t - 8|

10/3 = |t - 8|

t - 8 = 10/3 or t - 8 = -10/3

t = 10/3 + 8 t = -10/3 + 8

t = 11 1/3 t = 4 2/3

t = 11 1/3 corresponds to year 1990 + 11 = 2001

t = 4 2/3 corresponds to year 1990 + 4 = 1994

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