The annual carbon sequestration capacity of a geo-engineering facility is being scaled up to combat climate change. At the start of the project, the facility captures 12 500 tonnes of CO2\text{CO}_2CO2 per year. Exactly six years after the start of monitoring, the annual capacity has reached 18 200 tonnes.
A model assumes that the annual capacity increases by g% g \%\,g% each year, such that the sequence of capacities at the end of each year follows a geometric sequence.
Assuming the model:
Calculate the value of ggg, giving your answer to 2 decimal places.
According to the model, after N N\,N years of monitoring, the annual capacity first exceeds 50 000 tonnes. Determine, showing all steps in your working, the smallest integer value of NNN.
Practise Edexcel A Level Maths Sequences and Series with exam-style questions for A Level Maths. 156 questions covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
