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1 Pure Mathematics

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Question 597

A conservationist monitors the population of a rare lizard species on a remote island. The population, PPP, was recorded every 5 years from 1 January 2000 until 2025. The population size is modelled by the equation

P=kmn P = km^n P=kmn

where nnn is the number of years since 1 January 2000 and kkk and mmm are constants.

a.

Show that P=kmnP = km^nP=kmn can be written as log⁡10P=log⁡10k+nlog⁡10m\log_{10} P = \log_{10} k + n \log_{10} mlog10​P=log10​k+nlog10​m.

[2]
b.

The values of log⁡10P\log_{10} Plog10​P against nnn are plotted on a graph, and a line of best fit is drawn. The line of best fit passes through the points (0,1.48)(0, 1.48)(0,1.48) and (25,2.73)(25, 2.73)(25,2.73). Find estimates for the values of kkk and mmm, giving your answers to three significant figures.

[4]
c.

Use your model to predict the year in which the lizard population will first reach 2000.

[2]
d.

Comment on the reliability of your prediction in part (c).

[1]
Markscheme

1 Pure Mathematics Questions

  1. A Level
  2. /Maths
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