00:01
So in this problem, we're told on the day a video was posted online that five people watched the video.
00:05
And then the next day, the number of viewers had doubled.
00:08
And we're going to now assume the number of viewers continues to double each day.
00:11
Well, it seems like we have a sequence here.
00:13
So there was five people on the first day.
00:16
Well, if the number of people on the second day is to double it, that means we'd multiply this by two, which would be 10.
00:21
Which would mean on the third day, we'd multiply it by two and get 20.
00:25
And on the fourth day, again, we'd multiply by two and get 40.
00:28
So this pattern is going to continue to happen.
00:31
So in part a, we want to know on which day will 640 people see the video.
00:36
Now, in theory, we can continue to multiply by 2 until we get to 640.
00:40
But because we're multiplying by a constant, this is an example of a geometric sequence.
00:46
So we have a formula to find any term in the sequence.
00:49
It's a sub n is equal to a sub 1 times r raised to an n minus 1 power.
00:54
Now, let's fill in what we know.
00:56
When we know the a sub 1, that's the first term, is 5, r represents the rate that we're multiplying by, which in this case is 2, we want to know when there's 640 people.
01:07
So that's our a sub -n value, and we're trying to find the value of n, the number of days.
01:11
Okay, great.
01:12
So now we just have to solve this equation.
01:15
So to do that, i'm going to first start by dividing both sides of my equation by 5.
01:19
So it have 640, getting divided by 5, which is 128.
01:24
So now we have 128 equal to 2.
01:26
2 raised an n minus 1 power.
01:29
So is there a way we can rewrite 2 as a power or 2 to some power that equal to 128? well, we can.
01:36
2 to the 7th power is equal to 128.
01:38
So 2 to the 7 would be equal to 2 to the n minus 1 power.
01:43
So because their bases are the same, that tells us the exponents are equal.
01:47
So 7 would equal to n minus 1...