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QuestionUse the formula T=21x2+862x+15,552T=21 x^{2}+862 x+15,552 to find tuition costs for 2014, 2012, and project for 2020, 2022.

Studdy Solution

STEP 1

Assumptions1. The formula given is accurate and models the average cost of tuition and fees,, at private U.S. colleges for the school year ending xx years after2000. . The values of xx are whole numbers representing the years after2000.

STEP 2

To find the average cost of tuition and fees for the school year ending in a specific year, we need to substitute the value of xx in the given formula. The value of xx is the number of years after2000.For the year2014, x=2014−2000=14x =2014 -2000 =14.
Substitute x=14x =14 in the formula=21×142+862×14+15,552 =21 \times14^{2} +862 \times14 +15,552

STEP 3

Calculate the value of $$ for $x =14$.
=21×142+862×14+15,552=$31,716 =21 \times14^{2} +862 \times14 +15,552 = \$31,716So, the average cost of tuition and fees at private U.S. colleges for the school year ending in201 is $31,716.

STEP 4

The actual cost shown by the graph for the school year ending in2014 is not provided in the problem. Therefore, we cannot calculate how much the formula underestimates or overestimates the actual cost.

STEP 5

To project the average cost of tuition and fees for the school year ending in2020, we substitute x=2020−2000=20x =2020 -2000 =20 in the formula=21×202+862×20+15,552 =21 \times20^{2} +862 \times20 +15,552

STEP 6

Calculate the value of $$ for $x =20$.
=21×202+862×20+15,552=$41,512 =21 \times20^{2} +862 \times20 +15,552 = \$41,512So, the projected average cost of tuition and fees at private U.S. colleges for the school year ending in2020 is $41,512.

STEP 7

To find the average cost of tuition and fees for the school year ending in2012, we substitute x=2012−2000=12x =2012 -2000 =12 in the formula=21×122+862×12+15,552 =21 \times12^{2} +862 \times12 +15,552

STEP 8

Calculate the value of $$ for $x =12$.
=21×122+862×12+15,552=$29,520 =21 \times12^{2} +862 \times12 +15,552 = \$29,520So, the average cost of tuition and fees at private U.S. colleges for the school year ending in2012 is $29,520.

STEP 9

The actual cost shown by the graph for the school year ending in2012 is not provided in the problem. Therefore, we cannot calculate how much the formula underestimates or overestimates the actual cost.

STEP 10

To project the average cost of tuition and fees for the school year ending in2022, we substitute x=2022−2000=22x =2022 -2000 =22 in the formula=21×222+862×22+15,552 =21 \times22^{2} +862 \times22 +15,552

STEP 11

Calculate the value of $$ for $x =22$.
=21×22+862×22+15,552=$44,308 =21 \times22^{} +862 \times22 +15,552 = \$44,308So, the projected average cost of tuition and fees at private U.S. colleges for the school year ending in202 is $44,308.

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