How many songs can a digital music player hold? The data below represent the memory x and the number of songs n. Complete parts (a) through (f) below. Memory, x (gigabytes) A. OB. Number of Songs, An 80- An 19500- 8 1950 16 3900 32 7800 64 15600 19500 ..... C. (a) Plot the ordered pairs (x,n) in a Cartesian plane. Choose the correct graph on the right. An 8어 An 19500- (b) Show that the number of songs n is a linear function of the memory x. A linear function has a constant average rate of change. The average rate of change between (8,1950) and (16,3900) is 19500 (Type an integer or a decimal.)

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### Transcription and Explanation

#### Problem Statement
**How many songs can a digital music player hold?** The data below represent the memory \( x \) and the number of songs \( n \). Complete parts (a) through (f) below.

| Memory, \( x \) (gigabytes) | Number of Songs, \( n \) |
|-----------------------------|--------------------------|
| 8                           | 1950                     |
| 16                          | 3900                     |
| 32                          | 7800                     |
| 64                          | 15600                    |

#### Instructions
(a) **Plot the ordered pairs (x, n) in a Cartesian plane. Choose the correct graph on the right.**

Graphs labeled A, B, C, and D are provided. They all represent a plot with an x-axis labeled for memory in gigabytes and a y-axis labeled for the number of songs. The correct graph is option **D** where the points are plotted appropriately showing a positive relationship.

(b) **Show that the number of songs \( n \) is a linear function of the memory \( x \).**

A linear function has a constant *average rate of change*.

(c) **Calculate the average rate of change between (8, 1950) and (16, 3900).** 
- The average rate of change can be calculated as follows:
  \[
  \text{Average rate of change} = \frac{\Delta n}{\Delta x} = \frac{3900 - 1950}{16 - 8} = 243.75
  \]

**Graph Details:**
- **Graph D**: Plots the memory on the x-axis from 0 to 80 gigabytes and the number of songs on the y-axis from 0 to 19500. Points plotted (8, 1950), (16, 3900), (32, 7800), (64, 15600). The plot is linear indicating a consistent rate of increase for the number of songs as memory increases.

This presentation illustrates a direct and proportional relationship between the gigabytes of memory and the number of songs, forming a linear pattern on the graph.
Transcribed Image Text:### Transcription and Explanation #### Problem Statement **How many songs can a digital music player hold?** The data below represent the memory \( x \) and the number of songs \( n \). Complete parts (a) through (f) below. | Memory, \( x \) (gigabytes) | Number of Songs, \( n \) | |-----------------------------|--------------------------| | 8 | 1950 | | 16 | 3900 | | 32 | 7800 | | 64 | 15600 | #### Instructions (a) **Plot the ordered pairs (x, n) in a Cartesian plane. Choose the correct graph on the right.** Graphs labeled A, B, C, and D are provided. They all represent a plot with an x-axis labeled for memory in gigabytes and a y-axis labeled for the number of songs. The correct graph is option **D** where the points are plotted appropriately showing a positive relationship. (b) **Show that the number of songs \( n \) is a linear function of the memory \( x \).** A linear function has a constant *average rate of change*. (c) **Calculate the average rate of change between (8, 1950) and (16, 3900).** - The average rate of change can be calculated as follows: \[ \text{Average rate of change} = \frac{\Delta n}{\Delta x} = \frac{3900 - 1950}{16 - 8} = 243.75 \] **Graph Details:** - **Graph D**: Plots the memory on the x-axis from 0 to 80 gigabytes and the number of songs on the y-axis from 0 to 19500. Points plotted (8, 1950), (16, 3900), (32, 7800), (64, 15600). The plot is linear indicating a consistent rate of increase for the number of songs as memory increases. This presentation illustrates a direct and proportional relationship between the gigabytes of memory and the number of songs, forming a linear pattern on the graph.
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