Chapter 3.1, Problem 51AYU

(a)

To determine

To graph: The ordered pairs $\left(m,n\right)$ in a Cartesian plane. The following data represent the memory, $m$, and the number of songs, $n$.

$\begin{array}{|cc|}\hline \text{Memory},m(\text{gigabytes})& \text{Number}\text{of}\text{songs},n\\ 8& 1750\\ 16& 3500\\ 32& 7000\\ 64& 14,000\\ \hline\end{array}$

(b)

To determine

Whether the number of songs, $n$, is a linear function of the memory, $m$, or not.

The following data represent the memory, $m$, and the number of songs, $n$.

$\begin{array}{|cc|}\hline \text{Memory},m(\text{gigabytes})& \text{Number}\text{of}\text{songs},n\\ 8& 1750\\ 16& 3500\\ 32& 7000\\ 64& 14,000\\ \hline\end{array}$

(c)

To determine

The linear function that describes the relation between $m$ and $n$.

The following data represent the memory, $m$, and the number of songs, $n$.

$\begin{array}{|cc|}\hline \text{Memory},m(\text{gigabytes})& \text{Number}\text{of}\text{songs},n\\ 8& 1750\\ 16& 3500\\ 32& 7000\\ 64& 14,000\\ \hline\end{array}$

(d)

To determine

The domain of the linear function that describes the relation between $m$ and $n$.

The following data represent the memory, $m$, and the number of songs, $n$.

$\begin{array}{|cc|}\hline \text{Memory},m(\text{gigabytes})& \text{Number}\text{of}\text{songs},n\\ 8& 1750\\ 16& 3500\\ 32& 7000\\ 64& 14,000\\ \hline\end{array}$

(e)

To determine

To graph: The linear function $f\left(m\right)=218.75m$ in a Cartesian plane. The following data represent the memory, $m$, and the number of songs, $n$.

$\begin{array}{|cc|}\hline \text{Memory},m(\text{gigabytes})& \text{Number}\text{of}\text{songs},n\\ 8& 1750\\ 16& 3500\\ 32& 7000\\ 64& 14,000\\ \hline\end{array}$

(f)

To determine

The interpretation of the slope in the linear function that describes the relation between $m$ and $n$. The following data represent the memory, $m$, and the number of songs, $n$.

$\begin{array}{|cc|}\hline \text{Memory},m(\text{gigabytes})& \text{Number}\text{of}\text{songs},n\\ 8& 1750\\ 16& 3500\\ 32& 7000\\ 64& 14,000\\ \hline\end{array}$