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 Everyday Examples
 Base (of a Power):  The number or expression used as a factor for repeated multiplication.

Image source: http://www.geo.tsukuba.ac.jp/~hydro/labos/carbon14.gif

Carbon dating is a process that measures the age of an artifact based on its number of carbon-14 atoms. Carbon-14 has a half-life of 5,730 years, which is the time it takes for half of a substance to decay. For instance, if an artifact has 2000 carbon atoms right now, then it will have 1000 carbon atoms remaining in 5730 years (one half-life), and 500 carbon atoms in 11460 years (two half-lives), and so on. Therefore, the number of carbon atoms remaining can be predicted by the equation, c = i(1/2)n, where c is the number of carbon atoms, I is the number of carbon atoms initially, and n is the number of half-lives that have passed. Notice that the base, 1/2, represents the percentage of substance that remains after a given time period.


Image source: http://www.kn.pacbell.com/wired/democracy/money.gif

The amount of money in a savings account grows based on its principle (the amount of money put in at the start), the account's interest rate, and the time in years in which the money is left in the bank untouched. The amount of money, m, in an account earning 4% interest each year can be represented by the equation m = p(1.04)t, where p is the principle placed into the account and t is the length of time the money is left in the bank. The base of 1.04 means there will be 104% of the money from the previous year, accounting for the 4% of added interest.