A variable \(y\) is directly proportional to a variable quantity \(x^n\). Given that when \(x=2\), \(y=20.8\) and when \(x=3\), \(y=105.3\). Which one of the following is the constant of proportionality if it is greater than \(1\)?
1.3
Let \(y=kx^n\). Then \(k\cdot2^n=20.8\) and \(k\cdot3^n=105.3\). Dividing, \(\left(\frac{3}{2}\right)^n=\frac{105.3}{20.8}=5.0625=(1.5)^4\), so \(n=4\). Then \(k=\frac{20.8}{2^4}=\frac{20.8}{16}=1.3\). Hence the constant of proportionality is \(1.3\).
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