Question

A decibel is a logarithmic unit that can be used to measure the intensity of a sound. The function y = 10logx gives the intensity of a sound in decibels, where x is the ratio of the intensity of the sound to a reference intensity. The reference intensity is generally set at the threshold of hearing. Use the graphing utility to graph the decibel function.A whisper has a sound intensity of 30 decibels. Use your graph to help you complete the following statement. The sound intensity of a whisper is times the reference intensity.

Answer 1

Explanation:

Answer 2

The sound intensity of a whisper is 333.3 times the reference intensity

Explanation:

Given : The function
`y = 10logx` gives the intensity of a sound in decibels, where x is the ratio of the intensity of the sound to a reference intensity.

A whisper has a sound intensity of 30 decibels.

To find : Use your graph to help you complete the following statement. The sound intensity of a whisper is times the reference intensity.

Solution :

Graph is attached which shows their intersection at (1000,30).

We can also verify by substituting value.

We have given that a whisper has a sound intensity of 30 decibels.

Therefore, y=30 , Let log base 10

`y = 10logx`

`30 = 10logx`

`(30)/(10) =logx`

`3=logx`

Logarithmic property
`log_(x)b=a \Rightarrow b=x^a`

`x=10^3`

`x=1000`

The ratio of the intensity of the sound to a reference intensity is 1000 decibels

The sound intensity of a whisper is times the reference intensity is

`(1000)/(3)=333.33`

The sound intensity of a whisper is 333.3 times the reference intensity.