Exponential
Growth
A model for growth of a quantity for which the rate of growth
is directly proportional to
the amount present. The
equation for
the model is A = A_{0}b^{t} (where b > 1
) or A = A_{0}e^{kt} (where k is
a positive number representing the rate of growth). In both formulas
A_{0} is
the original amount present at time t = 0.
This model is
used for such phenomena as inflation or population growth.
For example, A = 7000e^{0.05t} is
a model for the exponential growth of $7000 invested at 5%
per year compounded
continuously.
See
also
Exponential decay, doubling
time, compound interest,
logistic growth, e
