Question 979943
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Picking a number and then trying it, or even picking several numbers and trying them is an ok strategy to get an idea of what is happening, but it is a poor strategy for proving a mathematical relationship.  For this you need to choose an arbitrary value and operate on that abstract quantity.


Let *[tex \Large x] represent the original distance, so *[tex \Large 2x] must be the doubled distance. Compare *[tex \Large f(x)] and *[tex \Large f(2x)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ \frac{800}{x^2}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(2x)\ =\ \frac{800}{(2x)^2}\ =\ \frac{200}{x^2}]


And therefore


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(2x)\ =\ \frac{1}{4}f(x)]


Hence, for any physically possible distance value x, the intensity is divided by 4 when the distance is doubled.


Extra credit.  What happens to the intensity when the distance is multiplied by some number n?  In other words, compare *[tex \Large f(x)] and *[tex \Large f(nx)] 


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \