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Exponentials and Logarithms

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Question 127

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. In the model, A=1.00×107A = 1.00 \times 10^7A=1.00×107 and B=−1.5B = -1.5B=−1.5.

A coordinate graph with log₁₀ P on the horizontal axis, log₁₀ N on the vertical axis, O at the origin, and a straight decreasing line between the axes.

a.

Find the gradient of the line and the value of log⁡10N\log_{10} Nlog10​N where the line meets the vertical axis.

[3]
b.

The company estimate they will sell 10,000 products. Find, according to the model, an estimate for the selling price.

[2]
c.

The company estimate they will make a profit of £650,000 from the product. Estimate their production costs per 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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