Exponential
Decay
A model for decay of a quantity for which the rate of decay
is directly proportional to
the amount present. The equation for
the model is A = A_{0}b^{t} (where
0 <
b < 1 )
or A = A_{0}e^{kt} (where k is
a negative number representing the rate of decay). In both formulas
A_{0} is
the original amount present at time t = 0.
This model is
used for phenomena such as radioactivity or depreciation. For
example, A = 50e^{–0.01t} is
a model for exponential decay of 50 grams of a radioactive
element that
decays at a rate of 1% per year.
See
also
Exponential growth, halflife, continuously
compounded interest, logistic growth, e
