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

• What is the formula for calculating doubling time?
• How does an increase in the growth rate affect the doubling time?
• Explain how integration can be used to solve problems involving exponential growth.

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.