00:01
Copyapot begins cooling in a room at time zero and it's given by the function t of t we want to find a function t of t which would be the inverse function that takes the temperature t as an input and outputs the time in t so let's think of this as um in terms of i'm going to think of this in terms of y and x temporarily so i'll do it.
00:40
Actually, we won't.
00:41
Well, let's use capital and lowercase t.
00:43
But we're going to interchange.
00:44
So this would be a lowercase t equals 102e to the negative point o2 capital t plus 7d8 to find the inverse.
00:55
We interchange the variables to solve because it's basically undo everything that the original function is doing.
01:02
So we'll subtract 78 to both sides.
01:12
Then we'll divide 102 to both sides.
01:15
Then we're going to take the natural log of both sides to get rid of the exponential base e, and then we're going to divide by negative 0 .2, and then we'll be equal to t, capital t...