Direct and Inverse Proportion

Direct and Inverse Proportion

IP 2

Two positive quantities follow these models:

Model A: \(y\propto\sqrt{x}\);
Model B: \(y^2\propto x^2\).

For both models, \(y=6\) when \(x=9\).

Find an equation for each model, expressing \(y\) in terms of \(x\).
Find the value of \(y\) predicted by each model when \(x=36\).
Explain why the predictions differ.

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Answer:(a) \(A\): \(y=2\sqrt{x}\), B: \(y=\frac23x\); (b) \(12\) and \(24\); (c) root scaling versus linear scaling.

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