What is the formula for exponential growth/decay?
Exponential growth and decay are mathematical processes used to model various natural phenomena, such as population growth, radioactive decay, and financial investments. The formulas for exponential growth and decay are expressed as follows:
Exponential Growth Formula
The formula for exponential growth is:
P(t) = P0 * ertWhere:
- P(t) is the population or quantity at time t
- P0 is the initial population or quantity
- e is the base of the natural logarithm (approximately 2.71828)
- r is the growth rate (expressed as a decimal)
- t is the time
Exponential Decay Formula
The formula for exponential decay is:
P(t) = P0 * e-rtWhere the variables have the same meanings as in the growth formula.
Applications
These formulas have wide applications in various fields, including science, finance, and engineering. Exponential growth is used to model phenomena that increase rapidly over time, while exponential decay is used for processes that decrease over time.
Conclusion
The formulas for exponential growth and decay provide a mathematical framework for understanding and modeling natural and man-made processes. By utilizing these formulas, scientists, researchers, and analysts can make predictions and informed decisions in a variety of fields.
