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.
231 exam-style questions on WJEC A Level Maths 3.4 Sequences and Series (A-level only), covering 3.4.1 Sequences and Series (A-level only), 3.4.2 Sequences and Series (A-level only), 3.4.3 Sequences and Series (A-level only), 3.4.4 Sequences and Series (A-level only), 3.4.5 Sequences and Series (A-level only), 3.4.6 Sequences and Series (A-level only), and 3.4.7 Sequences and Series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.