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 £50000 on January 1 2015 and the value changes by a factor of 0.800 each year.
(i) Find the value of the car on January 1 2019. (ii) Show that the value of the car on January 1 2022 is approximately £10500.
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.