Exercise 58 Page 11

For this exercise, we are give two equations that model the number of attendees (in thousands) for the NFL games. To find the number of people who attended the National Conference football games, we need to subtract the number who attended the American Conference games, A, from the total number of attendees T. N&=T-A &=T+(- A) This means that we need to know the terms of - A. A = -3.78x^3 + 58.96x^2 + 265.96x + 5257 ⇕ - A = 3.78x^3 - 58.96x^2 - 265.96x - 5257

Let's use the vertical method to line-up like terms and subtract.

Equation LHS	Cubic	Quadratic	Linear	Constant
T	-0.69x^3	55.83x^2	643x	10 538
- A	3.78x^3	-58.96x^2	-265.96x	-5257
T+(- A)	3.09x^3	-3.13x^2	377.04x	5281

This means that N is as follows. N = 3.09x^3 - 3.13x^2 + 377.04x + 5281 Now that we know the expression for the number of National Conference attendees, we need to find out how many years 2009 is since 2002 to determine what number to substitute for x. 2009-2002=7 Let's substitute, x=7, into our expression for N and evaluate it.

N = 3.09x^3-3.13x^2 + 377.04x + 5281

Substitute

x= 7

N =3.09( 7)^3-3.13( 7)^2 + 377.04( 7) + 5281

▼

Evaluate right-hand side

CalcPow

Calculate power

N =3.09(343)-3.13(49) + 377.04(7) + 5281

Multiply

Multiply

N = 1059.87-153.37+ 2639.28 + 5281

SubTerms

Subtract terms

N= 906.5 + 2639.28 + 5281

AddTerms

Add terms

N=8826.78

The exercise tells us that this number is in thousands, so let's multiply it by 1000 to get the number of attendees. 8826.78 * 1000 = 8 826 780 There were about 8 826 780 people who attended the National Conference football games in 2009.