The value of a car is modelled using the formula V=17100e−0.2t+2000V = 17100e^{-0.2t} + 2000V=17100e−0.2t+2000
Find the initial value of the car.
Given the model predicts that the value of the car is decreasing at a rate of £1000 per year at the instant when t=Tt = Tt=T, (i) Show that 3420e−0.2T=10003420e^{-0.2T} = 10003420e−0.2T=1000 and (ii) find the age of the car at this instant, giving your answer in years and months to the nearest month.
Practise Edexcel AS Level Maths Exponentials and Logarithms with exam-style questions for AS Level Maths. 41 questions covering 14.1 Exponential Functions, 14.2 y = e^x, 14.3 Exponential Modelling, 14.4 Logarithms, 14.5 Laws of Logarithms, 14.6 Solving Equations using Logarithms, 14.7 Working with Natural Logarithms, and 14.8 Logarithms and Non-Linear Data, matched to the Edexcel AS Level Maths (8MA0) specification and written in Paper 1 and Paper 2 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.