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. Explain in words each step to find the following question:

At what number(s) measures played would the sound level be at 80 decibels?

Answer 1

The numbers of measure of music played are 1 and 7

Explanation:

Given

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

Required

Solve for x when s = 80

Substitute 80 for x

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

Subtract 50 from both sides

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

`30= 10|x - 4|`

Divide through by 10

`(30)/(10)= (10|x - 4| )/(10)`

`3= |x - 4|`

Reorder

`|x - 4| = 3`

This can be split into

`x - 4 = 3` or
`x - 4 = -3`

Solve for x

`x = 4 + 3` or
`x = 4 - 3`

`x = 7` or
`x = 1`

Hence:

The numbers of measure of music played are 1 and 7