Do the values in the table represent a proportional relationship? x 1 2 3 4
y 2.5 5 7.5 10
All of the y-values are or are not a constant multiple of the corresponding x-values, so the relationship is or isn't proportional?

Using logarithmic rule:

then

Given that,

Sound intensity of a typical vacuum cleaner = 80 dB

Sound intensity of burst of eardrum = 160 dB

Let, I₁ and I₂ b e the intensity of typical vacuum and intensity of eardrum.

Use the formula:

As per the statement

The sound intensity of a typical vacuum cleaner is 80 dB (decibels).

⇒

Divide both sides by 10 we have;

Apply the logarithmic rules:

then;

⇒

Subtract 12 from both sides we have;

⇒                                    ......[A}

It is also given that: Sound intensity of 160 dB will burst an eardrum.

⇒  

Divide both sides by 10 we have;

Apply the logarithmic rules:

⇒

Subtract 12 from both sides we have;

⇒

⇒                                              ......[B]

We have to find how many times louder is the sound that will burst an eardrum than the sound of a vacuum cleaner.

⇒

Therefore, times louder is the sound that will burst an eardrum than the sound of a vacuum cleaner