The value, £VVV, of a car t t\,t years after it was bought on January 1 2015 is modelled by the equation V=AktV = Ak^tV=Akt where A A\,A and k k\,k are constants. The car was worth £20000 on January 1 2019 and £2500 on January 1 2022.
(i) Find k k\,k to 3 decimal places. (ii) Show that A A\,A is approximately £320000.
With reference to the model, interpret (i) The value of the constant AAA (ii) The value of kkk.
Using the model, find the year during which the value of the car first falls below £5000.
326 exam-style questions on Edexcel A Level Maths Sequences and Series, 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. Each one has a worked solution and a mark scheme showing where the marks go.