Verdopplungsformeln

Verdopplungsformeln, also known as doubling formulas, are mathematical expressions used to calculate the time required for a quantity to double in size. These formulas are particularly useful in fields such as biology, finance, and physics, where exponential growth is a common phenomenon. The most basic form of the doubling formula is derived from the exponential growth equation, which can be written as:

N(t) = N0 * e^(rt)

where:

- N(t) is the quantity at time t,

- N0 is the initial quantity,

- r is the growth rate,

- e is the base of the natural logarithm,

- t is the time.

To find the time it takes for the quantity to double, we set N(t) to 2N0 and solve for t:

2N0 = N0 * e^(rt)

2 = e^(rt)

ln(2) = rt

t = ln(2) / r

This formula shows that the time required to double is inversely proportional to the growth rate. For example, if the growth rate is 10% per year (r = 0.10), the doubling time would be approximately 7 years (ln(2) / 0.10). Verdopplungsformeln can also be applied to other types of growth, such as compound interest in finance, where the formula takes a slightly different form but follows the same principle of doubling.