Chapter 3.3, Problem 69E

(a) To find:

The x-intercept rounded to nearest tenth.

Solution:

x-intercept is $\left(\mathrm{4.5,0}\right)$

Concept:

To find the $x$-intercept of a graph, we should substitute $y=0$ in the given equation.

A point where a graph crosses the $x$-axis is called as $x$-intercept.

It is in the form of (a, 0).

To find the y-intercept of a graph, we should substitute x $=0$ in the given equation.

A point where a graph crosses the $y$-axis is called as $y$-intercept.

It is in the form of (0, b).

Explanation:

Given equation is $y=-7000x+\mathrm{31,800}$

Let y=0, $0=-7000x+31800$

$7000x=\mathrm{31,800}$

$x=\frac{31800}{7000}$

$x=4.54$ = 4.5

we get, x-intercept is $\left(\mathrm{4.5,0}\right)$

Conclusion:

x-intercept is $\left(\mathrm{4.5,0}\right)$

(b) To find:

The meaning of x-intercept rounded to nearest tenth.

Solution:

The number of analaog movie screens became zero after 5 years since 2009.

Concept:

To find the $x$-intercept of a graph, we should substitute $y=0$ in the given equation.

A point where a graph crosses the $x$-axis is called as $x$-intercept.

It is in the form of (a, 0).

To find the y-intercept of a graph, we should substitute x $=0$ in the given equation.

A point where a graph crosses the $y$-axis is called as $y$-intercept.

It is in the form of (0, b).

Explanation:

Given equation is $y=-7000x+\mathrm{31,800}$

Where x is number of years and y is number of analog movie screens

Let y=0, $0=-7000x+31800$

$x=4.54$ = 4.5 (rounded to nearest tenth)

we get, x-intercept is $\left(\mathrm{4.5,0}\right)$

This means, The number of analaog movie screens became zero after 5 years since 2009.

Conclusion:

x-intercept is $\left(\mathrm{4.5,0}\right)$

To determine

c) To use:

Part (b) to comment on your opinion of the limitations of using equations to model real data.