Difference between revisions of "Proportion"
m (→Inverse Proportion) |
|||
| Line 14: | Line 14: | ||
==Exponential Proportion== | ==Exponential Proportion== | ||
| + | A proportion in which one number is equal to a constant raised to the power of the other, or the logarithm of the other, is called an exponential proportion. It can be expressed as either:<br /> | ||
| + | <math>y = k^x.\,</math><br /> | ||
| + | <math>y = \log_k (x).\,</math><br /> | ||
| + | for some real number '''k''', where <math>k\ne 0,1</math>. | ||
Revision as of 19:25, 13 September 2007
| This is an AoPSWiki Word of the Week for Sep 13-19 |
Two numbers are said to be in proportion to each other if some numeric relationship exists between them. There are several types of proportions, each defined by a separate class of function.
Direct Proportion
Direct proportion is a proportion in which one number is a multiple of the other. Direct proportion between two numbers x and y can be expressed as:
where k is some real number.
The graph of a direct proportion is always linear.
Inverse Proportion
Inverse proportion is a proportion in which as one number's absolute value increases, the other's decreases in a directly proportional amount. It can be expressed as:
where k is some real number that does not equal zero.
The graph of an inverse proportion is always a hyperbola, with asymptotes at the x and y axes.
Exponential Proportion
A proportion in which one number is equal to a constant raised to the power of the other, or the logarithm of the other, is called an exponential proportion. It can be expressed as either:
for some real number k, where 
.
