- A new mineral has been discovered and is going to be mined over a number of years.
A model predicts that the mass of the mineral mined each year will decrease by \(15 \%\) per year, so that the mass of the mineral mined each year forms a geometric sequence.
Given that the mass of the mineral mined during year 1 is 8000 tonnes,
- show that, according to the model, the mass of the mineral mined during year 6 will be approximately 3550 tonnes.
According to the model, there is a limit to the total mass of the mineral that can be mined.
- With reference to the geometric series, state why this limit exists.
- Calculate the value of this limit.
It is decided that a total mass of 40000 tonnes of the mineral is required. This is going to be mined from year 1 to year \(N\) inclusive.
- Assuming the model, find the value of \(N\).