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.
308 exam-style questions on OCR (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.