Question

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 the 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.

Answer 1

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:

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