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 AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) 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.
