**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 = 7000*e*^{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*

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