Question

student enrollment in a county'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 is number of years since 1990.a. what is the enrollment since 1990 ( show your work)b. in what year(s) was the enrollment closest to 10,000? Explain how to find the answer

Answer 1

The 16 year period began from 1990 and the equation used to model the student enrolment is

n = -0.3It - 8I + 11

Where

n represents number of enrolments

t represents number of years

It - 8I means absolute value of t - 8 and it would always be positive.

a) We want to determine the enrolment for the past 16 years. This means that t = 16

We would substitute t = 16 into the given equation. It becomes

n = - 0.3I16 - 8I + 11

n = - 0.3*8 + 11

n = - 2.4 + 11 = 8.6

Since n is in thousands, the number of enrolments since 1990 would be

8.6 * 1000 = 8600

b) We would equate n = 10 into the given equation

10 = - 0.3It - 8I + 11

- 0.3It - 8I = 10 - 11 = - 1

It - 8I = - 1/ 0.3

t - 8 = 3.33

t = 3.33 + 8 = 11.33

So the number of years is 11

The year would be 2001 which is 11 years from 1990

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