key term - Doubling time

Definition

Doubling time is the period required for a quantity undergoing exponential growth to double in size. It is commonly used in contexts where the growth rate is constant.

5 Must Know Facts For Your Next Test

1. Doubling time can be calculated using the formula $T_d = \frac{\ln(2)}{k}$, where $k$ is the growth rate.
2. In problems involving exponential growth, doubling time helps predict future values of growing quantities.
3. The natural logarithm base $e$ and $\log(2)$ are key constants used in calculating doubling time.
4. Doubling time is inversely proportional to the growth rate; as the growth rate increases, doubling time decreases.
5. Applications of integration can be utilized to derive expressions and solve problems involving exponential growth and doubling times.

Review Questions

Related terms

Exponential Growth: A process where a quantity increases at a constant percentage rate over equal increments of time.

$e$ (Euler's Number): A mathematical constant approximately equal to 2.71828, which serves as the base for natural logarithms.

$\log$ Function: The logarithm function, often used to solve equations involving exponential functions by transforming multiplicative relationships into additive ones.