Answer
a. $26,317$
b. over-estimates by $44$
c. $30,568$
Work Step by Step
a. Use the formula $T=26x^{2}+819x+15,527$ to find the average cost of tuition and fees at private U.S. colleges for the school year ending in 2010. Because 2010 is 10 years after 2000, substitute 10 for $x$ in the given formula. Then use order of operations to find $T$.
$T=26x^{2}+819x+15,527$
$T=26(10)^{2}+819(10)+15,527$
$T=26(100)+819(10)+15,527$
$T=2,600+8,190+15,527 = 26,317$
The formula indicates that for the school year ending in 2010, the average cost of tuition and fees at private U.S. colleges was 26,317.
b. 26,317, the average cost of tuition and fees, is obtained by the given formula $T=26x^{2}+819x+15,527$. It overestimates the actual data value by $44$, or 26,273 - 26,317.
c. Because 2013 is 13 years after 2000, substitute 13 for $x$ in the given formula. Then use order of operations to find $T$.
$T=26x^{2}+819x+15,527$
$T=26(13)^{2}+819(13)+15,527$
$T=26(169)+819(13)+15,527$
$T=4,394+10,647+15,527 = 30.568$.
The formula indicates that for the school year ending in 2013, the average cost of tuition and fees at private U.S. colleges will be $30,568
