00:01
In order to find when these reserves are depleted of this 350 ,000 cubic meters of this mineral, we'll go ahead and start by coming up with a series here and we'll sum how much our usage of this mineral is.
00:16
So it starts off in 2009 at 5 ,000 cubic meters and there's an 8 % increase.
00:22
So the next term is going to be multiplied by adding 100 % on top of the 8 and 1 .08%.
00:30
Would be used in 2010.
00:33
In 2011, it would be another increase of 1 .08%.
00:39
And so we could write that as 1 .08 squared, since again, there were two increases of that 8%, and so on.
00:51
And we could look at this and identify this as a geometric series here with our initial amount 500, and then our rate of 1 .08%.
01:02
So we'll go ahead and write that now.
01:05
What's unique about this series is that we do not know the upper index here.
01:12
And so although it's going to start at zero because our first term, the rate is to the power zero, we really don't know that top term.
01:20
So i'm just going to leave it as a question mark.
01:23
Our a value, 5 ,000...