Chapter 3.3, Problem 3CYU

a.

To determine

The rate of change of prices from 2002 to 2004.

Answer to Problem 3CYU

  $2.005$ dollars per year

Explanation of Solution

Given:

The graph:

  

Concept Used:

Equation of the line passing through the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is given by $y-y_1=m\left(x-x_1\right)$ , where $\text{slope, }m=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

From the given graph is clear that the price in 2002 was 18.87 and in 2004 the price was 22.88.

The rate of change of a line between two points is given by the slope of the line.

So, the rate of change in price from 2002 to 2004 is given by

  $\begin{array}{c}\text{Rate of change}=\frac{22.88-18.87}{2004-2002}\\ =\frac{4.01}{2}\\ =2.005\end{array}$

Thus, the rate of change of price from 2002 to 2004 is $2.005$ dollars per year.

It means during the time period 2002 to 2004, the tickets average price was increasing at a rate of 2.005 dollars per year.

b.

To determine

The two year period that had a greater rate of change than 2002-2004.

Answer to Problem 3CYU

  $1998-2000$

Explanation of Solution

Given:

The graph:

  

Concept Used:

Equation of the line passing through the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is given by $y-y_1=m\left(x-x_1\right)$ , where $\text{slope, }m=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

The rate of change of a line between two points is given by the slope of the line.

From the given graph it is clear that the line segment between 1998 to 2000 has the greatest slope.

So, the time period when the rate of change is greater than 2002-2004 is in years 1998-2000.

c.

To determine

The years when the new stadium was built.

Answer to Problem 3CYU

  $2000-2002$

Explanation of Solution

Given:

The graph:

  

Concept Used:

Equation of the line passing through the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is given by $y-y_1=m\left(x-x_1\right)$ , where $\text{slope, }m=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

From the given graph, it is clear that the tickets average price dropped during the year 2000-2002. So, this is the time when the new stadium was built.