Doubling time

Definition

Doubling time is the period it takes for a quantity experiencing exponential growth to double in size or value. It can be calculated using the natural logarithm and the growth rate.

5 Must Know Facts For Your Next Test

1. Doubling time is commonly represented by $T_{d}$.
2. The formula for doubling time is $T_d = \frac{\ln(2)}{k}$, where $k$ is the growth rate.
3. $\ln(2) \approx 0.693$, which simplifies many calculations involving doubling time.
4. Doubling time can be derived from the exponential growth model $N(t) = N_0 e^{kt}$.
5. Understanding doubling time helps in analyzing phenomena like population growth, radioactive decay, and financial investments.

Review Questions

• What is the formula for calculating doubling time?
• How does the natural logarithm function play a role in determining doubling time?
• If a population has a growth rate of 3% per year, what would be its approximate doubling time?

Related terms

Exponential Growth:

A process that increases quantity over time at a rate proportional to its current value, often expressed as $N(t) = N_0 e^{kt}$.

Half-life:

The period it takes for a substance undergoing exponential decay to reduce to half its initial amount.

\ln (Natural Logarithm): \ln(x)$ represents the natural logarithm of x and is the inverse function of $e^x$ (exponential function).