Investigation 20 doubling time in exponential growth 2025

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Definition: Exponential Growth Model P(t)=P0(1+r)t. P0 is the initial population. r is the relative growth rate. t is the time unit.
Doubling times: This is the time it takes for a population to double in size. Doubling time=70/percentage growth rate.
At a 2% growth rate, both the actual and estimated doubling times are 35 years, resulting in a 0% variation.
The doubling time for the citys population growing at 11% per year is approximately 6.3 years using the natural logarithm formula. Alternatively, using the Rule of 72, the estimate is about 6.5 years. Both methods indicate a similar timeframe for the population to double.
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 (more roughly but roundly, dividing 72; see the rule of 72 for details and derivations of this formula).

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Doubling times Td given constant r% growth r%Td 7.0 10.24 7.5 9.58 8.0 9.01 8.5 8.506 more rows
Examining the doubling time can give a more intuitive sense of the long-term impact of growth than simply viewing the percentage growth rate. Some doubling times calculated with this formula are shown in this table. Simple doubling time formula: N ( t ) = N 0 2 t / T d.

how to calculate population doubling time