As the problem states, to solve this, we are going to use the equation [tex]L= log \frac{I}{I_{0} } [/tex]
where
[tex]L[/tex] is the loudness in dB
[tex]I[/tex] is the intensity of a sound
[tex]I_{0}[/tex] is the minimum intensity detectable by the human ear
We know for our problem that [tex]I=1.65*10^{-2}[/tex]; we also now that the minimum intensity detectable by the human ear is [tex]10^{-12)W/m^{2}[/tex], so [tex]I_{0}=10^{-12}[/tex]. Lets replace those values in our equation to find [tex]L[/tex]:
[tex]L=log \frac{1.65*10^{-2} }{10^{-12}} [/tex]
[tex]L=10.22dB[/tex]
Qe can conclude that since the explosion is under 100dB, it does not violates the regulation of the town. We used tow physical values to calculate the answer: the intensity of the sound of the explosion, [tex]I=1.65*10^{-2}W/m^2[/tex], and the minimum intensity detectable by the human ear [tex]I_{0}=10^{-12}W/m^{2}[/tex].
