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