Exponential growth is a specific type of growth where a value (or quantity) multiplies by a constant factor over equal intervals. This means that the increase in value in each interval is greater in absolute terms than in the previous interval. Exponential growth is a powerful concept and is common in nature, economics, demography, and technology.

The mathematical formula for exponential growth is:

V = P * (1 + r)^t

Where:

- V is the final value after t periods.
- P is the starting value (or the 'principal').
- r is the growth factor or growth rate (expressed as a decimal number).
- t is the number of periods.

It's important to note that the growth factor (r) must be divided by 100 if it's expressed as a percentage. For example, if the growth rate is 5%, then r is equal to 0.05 in the formula.

Let's take a look at an example. Suppose you start with an initial value (P) of 1000 and this value grows by 5% annually for 10 years. According to the formula, the final value (V) would be:

V = 1000 * (1 + 0.05)^10 = 1000 * 1.62889 = 1628.89

So after 10 years, your value would have grown to about 1629 (rounded to whole numbers).

Calculating exponential growth is not only useful for financial planning but also for understanding a variety of natural and social phenomena. Understanding exponential growth can, for example, help in understanding the spread of diseases, the growth of populations, or the growth of technologies.

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