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Exponentials and Logarithms

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Question 117

The world population, PPP (billion), is modelled by P=abtP = ab^tP=abt, where t t\,t is years since 1 April 1974. The linear relationship is log⁡10P=kt+0.6\log_{10}P = kt + 0.6log10​P=kt+0.6, where k>0k>0k>0.

A straight-line graph of log population against time

a.

Find, to 4 significant figures, the value of a a\,a and find the value of b b\,b in terms of kkk.

[3]
b.

With reference to the model interpret (i) the value of the constant aaa, (ii) the value of the constant b b\,b in terms of kkk.

[2]
c.

Find the world population, as predicted by the model, on 1 April 2020 in terms of kkk.

[2]
d.

Given the world population on April 2020 was 7.8 billion use your answer in part (c) to comment on the suitability of the model in terms of kkk.

[2]
Markscheme

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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