Here is a model for the number of students enrolled in U.S. public high schools as a function of time since 2000.

N = −0.033t^{2} + 0.46t + 13.37

In this formula N is the enrollment in millions of students, t is the time in years since 2000, and the model is applicable from 2000 to 2010.

(a) Calculate N(9).

(b) In what year was the enrollment the largest?

What was the largest enrollment?

(c) Find the average yearly rate of change in enrollment from 2004 to 2010.

Thank you for the opportunity to help you with your question!

(a) N(9) = -0.033*9^2+0.46*9+13.37=14.873

(b) when " −0.033t2 + 0.46t" < " −0.033(t+1)2 + 0.46(t+1)" , N reach the maximum.

then t < 6.47

then t =6

N= 14.973

(c) average yearly rate of change is [N(10)-N(4)]/6= 0.435

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