00:01
So we have been given a situation where the probability can be found by doing 1 minus e to the negative 0 .1t.
00:14
And we wanted to know after how many seconds, and i'm actually going to flip back to the question briefly here.
00:22
So we want to know within 10 minutes of midnight or 12 p .m.
00:28
Sorry, noon.
00:28
And we also want to know the probability that the car will arrive within 40 minutes.
00:32
So those two questions are fairly easy to do if we take a look at desmos.
00:39
So i've graphed the equation right here.
00:43
So if we come up here, maybe i'm going to change this, i'll make this an f of x.
00:48
So rather than using t, we are using x, but it makes it very easy for us to calculate f of 10 minutes.
00:56
So we would have approximately 0 .63, so that the 63 % probability.
01:04
And if we do the probability of arriving 40 minutes early, that would be 98 .168%.
01:12
So we can do that very easily.
01:15
And in going back up here, if i look at the equation, it wants to know as x or t gets larger and larger and larger, what does this value approach? well, you can visually estimate by looking here, and it seems to be getting close to one.
01:32
And it's easy to tell that because as we plug in larger and larger values for x, e to the negative 0 .1 times something is going to become e to the negative large, large, large values.
01:48
So what that means is this is really like saying, i'm going to just write it right here.
01:54
This is like saying 1 minus 1 over e to some power...