Doubling time

Definition

Doubling time is the period of time required for a quantity to double in size or value. It is often used in the context of exponential growth models.

5 Must Know Facts For Your Next Test

1. Doubling time can be calculated using the formula $T_d = \frac{\ln(2)}{r}$, where $r$ is the growth rate.
2. In an exponential growth model, doubling time remains constant as long as the growth rate stays unchanged.
3. $T_d = \frac{70}{r}$ is a simplified rule of thumb known as the Rule of 70, where $r$ is expressed as a percentage.
4. Doubling time is directly related to the base of natural logarithms ($e$) and involves logarithmic functions.
5. Understanding doubling time helps in analyzing real-world phenomena such as population growth, radioactive decay, and financial investments.

Review Questions

• What is the formula to calculate doubling time?
• How does changing the growth rate affect doubling time in an exponential model?
• Explain how doubling time relates to logarithmic functions.

Related terms

Exponential Growth: A process that increases quantity over time at a rate proportional to its current value.

Logarithmic Function: The inverse function of an exponential function, often used to solve equations involving exponentials.

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