00:01
Okay, in this problem, we have a machine with a decibel rating of 80 db, 80 decibels, and then we have a federal regulation that puts a maximum of 90 db.
00:18
So we have a maximum decibel rating of 90 db.
00:24
And we want to know how many more machines with this exact 80 db rating, can we add before we exceed our maximum here? and so what we could do is, well, first let's recall that the intensity as a function of the decibel level is just given by the reference intensity level times 10 raised to the decibel level divided by 10 db.
00:58
And so if we want to know how many machines we could have before we have the maximum, then we could just take the ratio of the maximum intensity to the intensity of our machine and use this equation with our decibel levels inserted to figure this out here.
01:18
So let's just insert these.
01:19
Well, i not is just going to cancel out because it's on the numerator and denominator.
01:22
So we're just going to be left with 10 to the beta max over.
01:28
10 db divided by 10 to the beta divided by 10 db which we could simplify i max over i equals 10 to the beta max minus beta over 10 db and we can just insert our values for beta here and we'll have 10 to the 90 minus 80 over 10...