Trying to get to the "root" of things. Sorry.
April 5, 2009 12:16 PM Subscribe
Totally naive math-filter. What is the relationship between percentage difference between two real numbers and the percentage difference between their squares?
posted by awenner to Science & Nature (8 answers total) 1 user marked this as a favorite
If I add 10% to x, then (x+10%)^2 will always be 21% larger than x^2. If I add 50% to x, then the squared difference will always be 225% Why? What's the relationship?
This is not a homework question. I'm actually studying for a standardized test which asks many questions along the lines of "if you increase the radius of a circle by 10% [or some such number], by what percentage will the total area increase?" Sometimes the value is given, sometimes it isn't, but the question runs more or less along the same lines.
One way of doing it is by plugging in the numbers and calculating it by hand: eg,
(1) let x=10.
(2) 10 + 10% = 11
(3) 10^2 = 100; 11^2=121
(4) 121 is 21% more than 10.
So, increasing the original number by 10% yields 21% on the other end.
In this context, it's easiest just to memorize the squares up to 20, but I'd like to know the "real" reason why this is. Bonus points if there's an elegant function that yields the difference when it's not so easily calculated in your head.