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 carbon14 atoms. Carbon14 has a halflife 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 halflife), and 500 carbon atoms in 11460 years (two halflives),
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 halflives
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.
