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Exponentials and Logarithms

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Question 66

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+Be6−1​t where A A\,A and B B\,B are constants.

A decreasing V-against-t curve passes through (0, 16) and (6, 8), with a dotted horizontal asymptote labelled y = k.

The graph passes through (0,16)(0, 16)(0,16) and (6,8)(6, 8)(6,8). y=ky = ky=k is an asymptote to the curve.

Find the values of AAA, B B\,B and kkk.

[5]
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Exponentials and Logarithms Questions

  1. A Level
  2. /Maths
  3. /Exponentials and Logarithms

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.

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