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Exponentials and Logarithms

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Question 97

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=0.005t+0.5\log_{10}P = 0.005t + 0.5log10​P=0.005t+0.5.

Graph of the linear relationship

a.

Show that P=100.5(100.005)tP = 10^{0.5}(10^{0.005})^tP=100.5(100.005)t.

[1]
b.

Hence find, to 4 significant figures, the value of a a\,a and the value of bbb.

[2]
c.

With reference to the model interpret (i) the value of the constant aaa, (ii) the value of the constant bbb.

[2]
d.

Find the world population, as predicted by the model, on 1 April 2020.

[2]
e.

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

[1]
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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