Lesson 4: Applications of Linear Equations

Math 10C Module 6: Lesson 4

Module 6: Linear Equations

Connect

Lesson Assessment

Complete the lesson quiz posted under the Quizzes link to the left in moodle or under the Assess tab and ensure your work in your binder (course folder) is complete.

Project Connection NOT ASSIGNED

This shows a photo of a young woman in a music store with several CDs in her hand.

Digital Vision/Thinkstock

Legal downloading has become an alternative to purchasing CDs to build your music collection. Some artists have started selling MP3s directly from their own websites. Sometimes up-and-coming artists offer a free song to help promote an album.

Your Project Connection for Lesson 4 is based on questions about a music downloading website. At this time, go to the Unit 4 Project and complete the Module 6: Lesson 4 component of the project.

Going Beyond

This shows a photo of a young woman wearing headphones and dancing to the music. The background is black with various coloured cells that resemble a graphic equalizer display.

iStockphoto/Thinkstock

Modern technology has made it even more convenient for us to listen to music wherever we are and whatever we may be doing. You can listen to music while you are riding the bus, doing your homework, working out at the gym, or doing household chores. You can take your entire music collection with you. In fact, you can even add the latest songs to your Wi-Fi enabled portable media player.

Listening to your favourite music can be a great way to spend your leisure time; however, prolonged exposure to loud music can threaten your hearing. Tiny hair cells in the cochlea of your ear are the receptors for hearing. Signals from these hair cells are translated into nerve impulses that are sent to the brain. Loud sounds destroy these tiny hair cells in the inner ear. Once about 25% of these cells disappear, you begin to experience hearing loss.

Hearing damage can occur in two ways:

Brief exposure to extremely loud sounds can cause permanent damage.
Consistent exposure to moderate-level loud sounds wears out the hair cells in the inner ear. Over time, permanent hearing loss occurs as these cells die.

Here is some data from an Internet search on safe use of iPods. Note: The abbreviation dB means decibel—a measure of the loudness of sound.

This chart shows safe exposure times to sounds of various volumes.

Percent of Volume Control	Maximum Listening Time per Day
Percent of Volume Control	Earbud	Isolator	Supra-Aural	iPod Stock Earphones
10–50%	no limit	no limit	no limit	no limit
60%	no limit	14 hours	no limit	18 hours
70%	6 hours	3.4 hours	20 hours	4.6 hours
80%	1.5 hours	50 minutes	4.9 hours	1.2 hours
90%	22 minutes	12 minutes	1.2 hours	18 minutes
100%	5 minutes	3 minutes	18 minutes	5 minutes
Maximum listening time per day using NIOSH damage-risk criteria. “Earbud” includes stock earphones and iPod in-ear earphones. “Isolator” includes Etymotic ER6i earphones and Shure E4c earphones. “Supra-Aural” includes Koss headphones that rest on top of the ear.

Your task is to analyze the data shown in the charts, answer the following questions, and provide a recommendation for safe use of personal music players as supported by mathematical evidence including your choice of equations, graphs, and data tables.

Is there a linear relationship between listening time and decibels? Explain how you know.
Is there a linear relationship between volume control and decibels? Explain how you know.
Is there a linear relationship between listening time and volume control? Explain how you know.
Would any graphs you create be continuous or discrete? Explain.
Can you figure out the domain and range here? Are there limits for this data?
What would be an appropriate independent variable? Explain.
Consider the sources of the data and your analysis. Make recommendations for safe use of personal music players.