Answer:
The sound intensity of a whisper is 333.3 times the reference intensity
Step-by-step explanation:
Given : The function [tex]y = 10logx[/tex] 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
[tex]y = 10logx[/tex]
[tex]30 = 10logx[/tex]
[tex]\frac{30}{10} =logx[/tex]
[tex]3=logx[/tex]
Logarithmic property [tex]log_{x}b=a \Rightarrow b=x^a[/tex]
[tex]x=10^3[/tex]
[tex]x=1000[/tex]
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
[tex]\frac{1000}{3}=333.33[/tex]
The sound intensity of a whisper is 333.3 times the reference intensity.
