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Modeling Data with Functions: Mastery Test

Select the correct answer.

A company manufactures school desks. The table shows the number of units that the company sold each month over a nine-month period beginning in January.

\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|}
\hline Month, [tex]$x$[/tex] & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline Units, [tex]$y$[/tex] & 800 & 500 & 400 & 300 & 200 & 300 & 450 & 600 & 800 \\
\hline
\end{tabular}

Which equation best models the situation?

A. [tex]$y=34 x^2-334 x+1,075$[/tex]

B. [tex]$y=-34 x^2+334 x+1,075$[/tex]

C. [tex]$y=-7 x+450$[/tex]

D. [tex]$y=7 x+450$[/tex]



Answer :

GinnyAnswer
To determine which equation best models the sales data given by the company over a nine-month period, we need to identify the relationship between the months [tex]\( x \)[/tex] and the units sold [tex]\( y \)[/tex]. This relationship can be modeled using a polynomial function, specifically a quadratic equation based on the choices provided.

We have the following data:
- Months [tex]\( x \)[/tex]: 1, 2, 3, 4, 5, 6, 7, 8, 9
- Units sold [tex]\( y \)[/tex]: 800, 500, 400, 300, 200, 300, 450, 600, 800

Let's derive the best fit quadratic equation [tex]\( y = ax^2 + bx + c \)[/tex].

Upon analysis, the coefficients [tex]\( a, b, \)[/tex] and [tex]\( c \)[/tex] for the best fit quadratic equation can be determined as follows:
- Coefficient [tex]\( a \approx 34 \)[/tex]
- Coefficient [tex]\( b \approx -334 \)[/tex]
- Constant term [tex]\( c \approx 1,075 \)[/tex]

These coefficients most closely match the equation [tex]\( y = 34x^2 - 334x + 1,075 \)[/tex].

Therefore, the best equation to model the given data is:

A. [tex]\( y = 34x^2 - 334x + 1,075 \)[/tex]

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