I just started reading my physics book again, and one of the very first things it talks about is proportionality. I understand the concept that two things are proportional if one gets multiplied by a certain factor and the other one has to be multiplied by the same factor. For instance, if John makes $10 per hour and works 3 hours, he makes $30. But if he works 6 hours we know that he makes $60 because the money he earns is proportional to the time he spends working.(adsbygoogle = window.adsbygoogle || []).push({});

However, it's when exponents are introduced into the proportion that I get confused. My physics book states that

"the area of a circle is proportional to the square of the radius (A=[tex]\pi[/tex]r[tex]^{2}[/tex], so A [tex]\propto[/tex] r[tex]^{2}[/tex]). The area must increase by the same factor as the radius squared, so if the radius doubles, the area increases by a factor of 2[tex]^{2}[/tex]=4"

I don't understand this. Why are they talking about the radius doubling when the proportionality deals with the radius squared? Shouldn't it be if the radius squared doubles, then the area also doubles? The way they are saying it is like... if the radius doubles, then the area quadruples.

I guess I *kind of* understand what they are doing. They are taking the exponent from the proportionality and using it on the multiplier, but why?

Why isn't it just "if the radius squared is multiplied by a factor, then the area is multiplied by the same factor" ?

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# Homework Help: Problem understanding proportions with exponents

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