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

Answer:

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

Step-by-step 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