2024 IGCSE Additional Mathematics May/June 0606/13 Q5

2024 IGCSE Additional Mathematics May/June 0606/13 Q5

6 marks

When \(\mathrm{e}^{2y}\) is plotted against \(x^3\), a straight line graph that passes through the points \((2,5)\) and \((6.4,7.2)\) is obtained.

  1. Find \(y\) in terms of \(x\).[4]
  2. Find the values of \(x\) for which \(y\) exists.[2]

Solution:

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Answer:(a) \(y=\dfrac12\ln\!\left(\dfrac{x^3}2+4\right)\). (b) \(x>-2\).

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