Chapter 7.1, Problem 25E

(a)

To determine

To Make: The table showing the numbers of song that will fit on the MP3 player when the average size of the song is $2\text{MB},2.5MB,3MB,5MB$

Answer to Problem 25E

  $y=\frac{10}{x}$

Explanation of Solution

Given: The number of songs that can be stored by the MP3 player varies inversely with the average size $x$ of a song. A certain MP3 player can store $2500$ songs when the average size of the song is $4$ megabyte.

Let $x$ be the average size of the song and $y$ be the number of songs

We know that Equation for inverse variation: $xy=a,y=\frac{a}{x}$

Put $x=4,y=2500$

  $\begin{array}{l}y=\frac{a}{x}\\ 2500=\frac{a}{4}\\ a=10,000\end{array}$

Substitute $a=10,000$ in inverse variation equation

Thus

  $y=\frac{10,000}{x}$

Now taking the value of $x$ are $2\text{MB},2.5MB,3MB,5MB$ and making the table of the function.

i.e.

  

(b)

To determine

To Explain: What happens to the number of songs as the average song size increases?

Answer to Problem 25E

As average size of the song increases, the number of song that can be stored decreases.

Explanation of Solution

Given: The number of songs that can be stored by the MP3 player varies inversely with the average size $x$ of a song. A certain MP3 player can store $2500$ songs when the average size of the song is $4$ megabyte.

As the number of songs that can be stored by the MP3 player varies inversely with the average size $x$ of a song

As average size of the song increases, the number of song that can be stored decreases.