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1.8 Exponentials and Logarithms

1.8 Exponentials and Logarithms

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Question 41

The value of a car is modelled using the formula V=17100e−0.2t+2000V = 17100e^{-0.2t} + 2000V=17100e−0.2t+2000

a.

Find the initial value of the car.

[1]
b.

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.

[6]
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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