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1.8 Exponentials and Logarithms

1.8 Exponentials and Logarithms

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Question 43

Michael's car is valued after 2 years and after 5 years. V=Ae−ktV = Ae^{-kt}V=Ae−kt.

Time (years)25
Value (£)4720029200
a.

Explain what the value of A A\,A represents.

[1]
b.

Show that ln⁡V=ln⁡A−kt\ln V = \ln A - ktlnV=lnA−kt

[1]
c.

Calculate the value of A A\,A and the value of kkk

[4]
d.

Use the model to predict the value of the car after 10 years.

[2]
Markscheme

1.8 Exponentials and Logarithms Questions

  1. A Level
  2. /Maths
  3. /1.8 Exponentials and Logarithms

104 exam-style questions on OCR (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.

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