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.)
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.)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbea8501a-47cf-43c6-9fd0-955ec556d935%2F96668dab-5a65-49be-8385-563a7e013e2b%2F1w7a14l_processed.png&w=3840&q=75)
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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