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Q35.

Expert-verifiedFound in: Page 158

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.

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 $v=3$.

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

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 | $0.45$ | $\left(3,0.45\right)$ |

The plot of the points $\left(v,p\right)$ is:

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

Therefore, the graph of the equation is:

The graph of the equation is:

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

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 $2.1$.

The condition on** **number of viewers is that number of viewers cannot 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.

**The table shows the cost of picking your own strawberries at a farm.**

Number of Pounds | 1 | 2 | 3 | 4 |

Total Cost ($) | 1.25 | 2.50 | 3.75 | 5.00 |

**a. Graph the data.**

**b. Write an equation in function notation to describe this relationship.**

**c. How much would it cost to pick 6 pounds of strawberries?**

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