SOLUTION: Sometimes mathematical models other than linear models are appropriate for data. Suppose that an equation of the form y=ax^2+bx+c is an appropriate model for the ordered pairs (x1,

Question 721765: Sometimes mathematical models other than linear models are appropriate for data. Suppose that an equation of the form y=ax^2+bx+c is an appropriate model for the ordered pairs (x1,y1),(x2,y2), and (x3,y3). Then it is necessary to find the values of a,b, and c such that the given ordered pairs are solutions of the equation y=ax^2+bx+c. To do so, substitute each ordered pair into the equation. Solving the resulting system of three linear equations in three unknowns will give the required values of a, b, and c.
The tables gives the total beef supply (in billions of pounds) in the United States in each of the years listed.
Total U.S Beef Supply
Year- Beef Supply (billions of pounds)
1999- 29.8
2001- 29.9
2003- 30.1
(a) Write the data as ordered pairs of the form (x,y), where y is the beef supply (in billions of pounds) in the year x (x=0 represents 1999).
(b) Find the values of a, b, and c such that the equation y=ax^2+bx+c models this data.
(c) According to the model, what was the U.S. beef supply in 2002?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Year- Beef Supply (billions of pounds)
1999- 29.8
2001- 29.9
2003- 30.1
(a) Write the data as ordered pairs of the form (x,y), where y is the beef supply (in billions of pounds) in the year x (x=0 represents 1999).
You have 3 points:
(0,29.8)
(2,29.9)
(4,30.1)
========================
(b) Find the values of a, b, and c such that the equation y=ax^2+bx+c models this data.
:::::::::::::::ax^2 + bx + c = y
(0,29.8) gives: 0 + 0 + 1 = 29.8
(2,29.9) gives: 4a + 2b + 1 = 29.9
(4,30.1) gives: 16a+ 4b + 1 = 30.1
----
Using a TI-84 I get:
a = 1/80
b = 1/40
c = 149/5
----
Equation:
y = (1/80)x^2 + (1/40)x + (149/5)
-----------------------------------------
(c) According to the model, what was the U.S. beef supply in 2002?
f(3) = 29.988
===================
Cheers,
Stan H.
================
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