Q19-write a note on doubling(time) the …

Doubling time is the amount of time it takes for a given quantity to double in size or value at a constant growth rate. We can find the doubling time for a population undergoing exponential growth by using the Rule of 70. To do this, we divide 70 by the growth rate (r).

The doubling time is time it takes for a population to double in size/value. It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things that tend to grow over time. When the relative growth rate (not the absolute growth rate) is constant, the quantity undergoes exponential growth and has a constant doubling time or period, which can be calculated directly from the growth rate.

This time can be calculated by dividing the natural logarithm of 2 by the exponent of growth, or approximated by dividing 70 by the percentage growth rate[1] (more roughly but roundly, dividing 72; see the rule of 72 for details and derivatiatives of this formula).

The doubling time is a characteristic unit (a natural unit of scale) for the exponential growth equation, and its converse for exponential decay is the half-life.