The value of a car is modelled using the formula V=18000e−0.2t+2000V = 18000e^{-0.2t} + 2000V=18000e−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 £R R\,R per year at the instant when t=Tt = Tt=T, and that the car is 6 years 3 months old at this instant, (i) Show that e−0.2T=e−1.25e^{-0.2T} = e^{-1.25}e−0.2T=e−1.25 and (ii) find RRR, giving your answer to the nearest pound.
277 exam-style questions on Edexcel A Level Maths Exponentials and Logarithms, 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. Each one has a worked solution and a mark scheme showing where the marks go.