SOLUTION: Using the function, what happens to the intensity if you double the distance from the light source? (Consider a certain distance and use the function to determine the intensity. T

Algebra ->  Rational-functions -> SOLUTION: Using the function, what happens to the intensity if you double the distance from the light source? (Consider a certain distance and use the function to determine the intensity. T      Log On


   

Question 979943: Using the function, what happens to the intensity if you double the distance from the light
source? (Consider a certain distance and use the function to determine the intensity. Then
double the distance and determine the intensity. Do this for several pairs of distances. You
should see a pattern develop. Express that pattern. Hint: you should be able to multiply
the first intensity by some number and get the second intensity.)
Function: f(x) =800/x^2
Distance from sensor (cm) 20 30 40 50 60 70 80 90 100

Intensity Gauge Reading 1 .86 .48 .39 .27 .19 .16 .13 .03

I doubled the distance but I kept getting a differing pattern each time. Any help would be appreciated.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


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 represent the original distance, so must be the doubled distance. Compare and





And therefore



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 and

John

My calculator said it, I believe it, that settles it