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Expert-verified Found in: Page 158 ### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801 # The number of people who watch a singing competition can be given by $p=0.15v$, where $p$ represents the number of people in millions who saw the show and $v$ is the number of potential viewers in millions.a. Make a table of values for the points $\left(v,p\right)$.b. Graph the equation.c. Use the graph to estimate the number of people who saw the show if there are 14 million potential viewers.d. Explain why it would not make sense for $v$ to be a negative number.

a. The table of values for the points $\left(v,p\right)$ is:

 $v$ $p$ $\left(v,p\right)$ 0 0 $\left(0,0\right)$ 1 $0.15$ $\left(1,0.15\right)$ 2 $0.3$ $\left(2,0.3\right)$ 3 $0.45$ $\left(3,0.45\right)$

b. The graph of the equation is: c. when the number of potential viewers are 14 million then the number of people who saw the show is $2.1$ million.

d. The reason why it would not make sense for $v$ to be a negative number is that the $v$ represents the number of potential viewers in millions and the number of potential viewers cannot be negative therefore width="10" style="max-width: none; vertical-align: -4px;" $v$ cannot be negative number.

See the step by step solution

## Part a. Step 1. Find the values of p for some values of v.

Find the value of $p$ for $v=0$.

localid="1647264931646" $p=0.15v\phantom{\rule{0ex}{0ex}}=0.15\left(0\right)\phantom{\rule{0ex}{0ex}}=0$

Find the value of $p$ for $v=1$.

localid="1647264936019" $p=0.15v\phantom{\rule{0ex}{0ex}}=0.15\left(1\right)\phantom{\rule{0ex}{0ex}}=0.15$

Find the value of $p$ for $v=2$.

localid="1647261383774" $p=0.15v\phantom{\rule{0ex}{0ex}}=0.15\left(2\right)\phantom{\rule{0ex}{0ex}}=0.3$

Find the value of $p$ for $v=3$.

$p=0.15v\phantom{\rule{0ex}{0ex}}=0.15\left(3\right)\phantom{\rule{0ex}{0ex}}=0.45$

## Part a. Step 2. Make a table of values for the points v,p.

The table of values for the points $\left(v,p\right)$ is:

 $v$ $p$ $\left(v,p\right)$ 0 0 $\left(0,0\right)$ 1 $0.15$ $\left(1,0.15\right)$ 2 $0.3$ $\left(2,0.3\right)$ 3 $0.45$ $\left(3,0.45\right)$

## Part b. Step 1. Plot the points v,p from the above table.

The plot of the points $\left(v,p\right)$ is: ## Part b. Step 2. Graph the equation.

Draw the graph of the equation by joining the plotted points.

Therefore, the graph of the equation is: ## Part c. Step 1. Observe the graph of the equation.

The graph of the equation is: From the graph it can be noticed that when $v=14$, $p=2.1$.

## Part c. Step 2. Use the graph to estimate the number of people who saw the show if there are 14 million potential viewers.

From the graph it can be noticed that when $v=14$, $p=2.1$.

That implies when the number of potential viewers are 14 million then the number of people in millions who saw the show is $2.1$.

## Part d. Step 1. State the condition on number of viewers.

The condition on number of viewers is that number of viewers cannot be a negative number.

## Part d. Step 2. State the reason why it would not make sense for v to be a negative number.

The reason why it would not make sense for $v$ to be a negative number is that the $v$ represents the number of potential viewers in millions and the number of potential viewers cannot be negative therefore $v$ cannot be negative number. ### Want to see more solutions like these? 