Exponentials and Logarithms
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Question 112
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 log10P=0.008t+0.6\log_{10}P = 0.008t + 0.6log10P=0.008t+0.6.
a.[3]
Find the exact value of a a\,a and the exact value of bbb.
b.[2]
With reference to the model interpret (i) the value of the constant aaa, (ii) the value of the constant bbb.
c.[2]
Find the world population, as predicted by the model, on 1 April 2020.
d.[1]
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.
Exponentials and Logarithms Questions
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.