Question

During a musical an orchestra is playing. As the music plays, the volume changes in the beginning of the piece can be modeled by the equation s = 10│x - 4│+ 50 where s represents the sound level in decibels and x represents the number of measures of music played. At what number(s) measures played would the sound level be at 80 decibels?

Answer 1

The sound level would be at 80 decibels at 1 or 7 number of measures played

Explanation:

Equations with Absolute Values

We have the function s to represent the sound level in decibels:

`s = 10|x - 4|+ 50`

Where x is the number of measures of the music played.

We are required to find the value of x that makes s=80 decibels. We have to find the equation:

`10|x - 4|+ 50 =80`

Subtracting 50:

`10|x - 4| =80-50`

`10|x - 4| =30`

Dividing by 10:

`|x - 4| =30/10=3`

`|x - 4| =3`

For the absolute value be equal to 3, its argument could be positive or negative:

`x-4=3`

Or

`x-4=-3`

This leads us to two solutions:

`x=3+4=7`

x=7

Or

`x-4=-3`

`x=4-3=1`

x=1

The sound level would be at 80 decibels at 1 or 7 number of measures played