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Exponentials and Logarithms

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Question 23

A company model the number of products they will sell NNN, and the price PPP, by N=APBN = AP^BN=APB. The graph shows the linear relationship between log⁡10N\log_{10} Nlog10​N and log⁡10P\log_{10} Plog10​P. The line meets the vertical axis at 7.4 and has a gradient of -1.50.

A coordinate graph showing a descending straight line, with log₁₀P on the horizontal axis, log₁₀N on the vertical axis, and the origin labelled O.

a.

Find, to the 3 significant figures, the value of A A\,A and the value of BBB.

[3]
b.

The company sets a selling price at £36.00. Find, according to the model, an estimate for the number of products the company will sell.

[2]
c.

The company estimate their production costs to be £12 per product. Estimate the profit the company will make from the product.

[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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