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ahrayia [7]
1 year ago
15

1. In 2009 the number of vehicle sales in the United States was 10,602 thousand and in 2013 it was15,884 thousand.a. Determine t

he average rate of change (slope) from 2009 to 2013.b. If x is the number of years since 2009 and f(x) is the number of vehicles sold, find theequation of the line through these two points.C. Assuming f(x) is a linear function, use the equation to predict the number of vehiclessold in 2016.
Mathematics
1 answer:
lord [1]1 year ago
6 0

Answer:

• (a)1320.5 thousand per year

,

• (b)f(x)=1320.5x+10602

,

• (c)f(7)=19846 thousand

Explanation:

Sales in the year 2009 = 10,602 thousand

Sales in the year 2013 = 15,884 thousand.

(a)Average rate of change (slope) from 2009 to 2013.

\begin{gathered} =\frac{15,884-10,602}{2013-2009} \\ =\frac{5282}{4} \\ =1320.5\text{ thousand per year} \end{gathered}

(b)If x is the number of years since 2009 and f(x) is the number of vehicles sold

When x=0, f(x)=10,602 thousand

The slope-intercept form of the equation of a line is: y=mx+b

\begin{gathered} 10602=1320.5(0)+b \\ b=10602 \end{gathered}

The equation of the line through these two points is:

f(x)=1320.5x+10602

(c)Number of vehicles sold in 2016.

2016-2009=7

Therefore, when x=7

The number of vehicles sold, f(x) will be:

\begin{gathered} f(7)=1320.5(7)+10602 \\ =19845.5 \\ \approx19846\text{ thousands vehicle} \end{gathered}

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