00:01
Hi there, so the function that we are given for this is that the decimal level is equal to 10 times the decimal logarithm of the intensity and this plus 120.
00:21
So for the first question in here, we are asked to express the intensity as a function of d.
00:27
So what we need to do is to take the expression that we are given and then solve for the intensity.
00:35
So first of all, we pass this 120 to subtract to the d.
00:43
So there will be d minus 120.
00:47
Now we divide this by 10.
00:49
Then we are left with the logarithm in base 10 of the intensity.
00:56
Now what we need to do is to apply the inverse function of the logarithm in base 10, which what we need to do is to apply 10 to the something because let me put it in here, 10 of x is the inverse of the logarithm in base t of x.
01:18
So with that said, we will have that this is 10 to d minus 120 divided by 10 is equal to the intensity.
01:30
So with this we have the intensity in function of d.
01:37
Now, for part b of this problem, we need to show that when the distance, when d increases by a factor of 20, the intensity increases by a factor of 100.
01:53
Okay.
01:54
So, okay.
01:58
So what the condition is that d is now d plus 20, because we increase that by 20.
02:11
So if we do, if we substitute that into the previous expression, we will have.
02:16
But intensity is 10.
02:20
D is now d plus 10...