Recovering a power law from two measurements

Recovering a power law from two measurements

Secondary 3
5 marks
TGM Original Questions

Positive variables \(x\) and \(y\) satisfy \(y=ax^n\), where \(a>0\). When \(x=2\), \(y=12\), and when \(x=8\), \(y=192\).

  1. State suitable axes for a straight-line graph and identify its gradient and vertical intercept.[2]
  2. Use the two measurements to find \(a\) and \(n\).[3]

Solution:

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Answer:(a) \(\lg y\) against \(\lg x\); gradient \(n\), intercept \(\lg a\). (b) \(a=3,\ n=2\).

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