Question 75
The value of a car t t\,t years after it was purchased, where V V\,V is the value of the car in thousands of pounds, is modelled by the formula V=A+Be−16t\displaystyle V = A + Be^{\frac{-1}{6}t}V=A+Be6−1t where A A\,A and B B\,B are constants.
The graph passes through (0,18)(0, 18)(0,18) and (6,7)(6, 7)(6,7). y=ky = ky=k is an asymptote to the curve.
a.[3]
Show that 11=B(1−e−1)11 = B(1-e^{-1})11=B(1−e−1).
b.[2]
Hence find the values of AAA, B B\,B and kkk.
Exponentials and Logarithms Questions
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.