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.
Find, to 4 significant figures, the value of a a\,a and the value of bbb
With reference to the model interpret (i) the value of the constant aaa, (ii) the value of the constant bbb.
Find the world population, as predicted by the model, on 1 April 2020.
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.
Practise Edexcel A Level Maths Exponentials and Logarithms with exam-style questions for A Level Maths. 41 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
