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# Double Time Formula

The time required for any quantity to transform into a double-sized or value is known as doubling time. It can be applied to calculate the consumption of goods, compound interest, population growth, inflation, resource extraction, the volume of malignant tumours, and many other things that can expand over a period of time. The time is calculated by dividing the natural logarithm of 2 by the exponent of growth or approximated by dividing 70 by the percentage growth rate, i.e. 70/r. With the help of a constant growth rate, we can easily calculate the double-time by the below-given formula.

$\LARGE T_{d}=\frac{\log 2}{\log (1+r)}$

Where,

$$\begin{array}{l}T_{d}\end{array}$$
= doubling time
r = content growth rate

### Solved Example

Question: Find the doubling time of a constant growth rate of 13%.
Solution:

Given constant growth rate, r = 13% =
$$\begin{array}{l}\frac{13}{100}\end{array}$$
= 0.13

Doubling time formula,

$$\begin{array}{l}T_{d}\end{array}$$
=
$$\begin{array}{l}\frac{log 2}{log(1+0.13)}\end{array}$$

$$\begin{array}{l}T_{d}\end{array}$$
= 5.67.
Hence, the doubling time is 5.67.