Chapter 3.1, Problem 57PPS

(a)

To determine

Graph the equation $\text{p =}\frac{\text{15}}{\text{4}}\text{t}\text{+}\text{66}$

Answer to Problem 57PPS

Explanation of Solution

Given:

The percent of teens who play online games can be modeled by $\text{p =}\frac{\text{15}}{\text{4}}\text{t}\text{+}\text{66}$ . P is the percent of student and t represent time in years since 2000.

Concept Used:

First make a table to draw the graph $\text{p =}\frac{\text{15}}{\text{4}}\text{t}\text{+}\text{66}$

Calculation:

Table

$\text{p =}\frac{\text{15}}{\text{4}}\text{t}\text{+}\text{66}$

$\text{t}$ $\text{p =}\frac{\text{15}}{\text{4}}\text{t}\text{+}\text{66}$ $\text{p }$ $\text{(t,p)}$ 0 $\begin{array}{l}\text{p =}\frac{\text{15}}{\text{4}}·0\text{+}\text{66}\\ \text{p}\text{=}\text{66}\end{array}$ $\text{66}$ $\text{(0}\text{,}66\text{)}$ 8 $\begin{array}{l}\text{p =}\frac{\text{15}}{\text{4}}·8\text{+}\text{66}\\ \text{p}\text{=}\text{30}\text{+}\text{66}\text{=}\text{96}\end{array}$ $\text{96}$ $\text{(8}\text{,}96\text{)}$

Thus,

(b)

To determine

Use the graph to estimate the percent of students playing the games in 2008

Answer to Problem 57PPS

In 2008 the percent of student is 96.

Explanation of Solution

Given:

The percent of teens who play online games can be modeled by $\text{p =}\frac{\text{15}}{\text{4}}\text{t}\text{+}\text{66}$ . P is the percent of student and t represent time in years since 2000.

Concept Used:

Use the graph to estimate the percent of students playing the games in 2008

Calculation:

The graph of the equation: $\text{p =}\frac{\text{15}}{\text{4}}\text{t}\text{+}\text{66}$

We can calculate the percent of student in 2008 algebraically. Equation: $\text{p =}\frac{\text{15}}{\text{4}}\text{t}\text{+}\text{66}$ $\text{p}$ is the percent of student and $\text{t}$ represents time in years since 2000. In 2008 means t = 8 years $\begin{array}{l}\text{p =}\frac{\text{15}}{\text{4}}\text{t}\text{+}\text{66}\\ \text{p =}\frac{\text{15}}{\text{4}}·8\text{+}\text{66}\\ \text{p}\text{=}\text{30}\text{+}\text{66}\text{=}\text{96}\end{array}$

In 2008 the percent of student is 96.

Thus, in 2008 the percent of student is 96.