How to Calculate Doubling Time
Check that the growth rate is small enough for this method., Multiply the growth rate by 100 to express it as a percentage., Divide 70 by the percentage growth rate., Convert your answer to the desired unit of time.
Step-by-Step Guide
-
Step 1: Check that the growth rate is small enough for this method.
Doubling time is a concept used for quantities that grow exponentially.
Interest rates and the growth of a population are the most common examples used.
If the growth rate is less than about
0.15 per time interval, we can use this fast method for a good estimate.If the problem doesn't give you the growth rate, you can find it in decimal form using CurrentQuantity−PastQuantityPastQuantity{\displaystyle {\frac {CurrentQuantity-PastQuantity}{PastQuantity}}}.
Example 1:
The population of an island grows at an exponential rate.
From 2015 to 2016, the population increases from 20,000 to 22,800.
What is the population's growth rate? 22,800
- 20,000 = 2,800 new people. 2,800 ÷ 20,000 =
0.14, so the population is growing by
0.14 per year.
This is small enough that the estimate will be fairly accurate. -
Step 2: Multiply the growth rate by 100 to express it as a percentage.
Most people find this more intuitive than the decimal fraction.
Example 1 (cont):
The island had a growth rate of
0.14, written as a decimal fraction.
This represents
0.141{\displaystyle {\frac {0.14}{1}}}.
Multiply the numerator and denominator by 100 to get
0.141x100100=14100={\displaystyle {\frac {0.14}{1}}x{\frac {100}{100}}={\frac {14}{100}}=} 14% per year. , The answer will be the number of time intervals it takes the quantity to double.
Make sure you express the growth rate as a percentage, not a decimal, or your answer will be off. (If you're curious why this "rule of 70" works, read the more detailed method below.) Example 1 (cont):
The growth rate was 14%, so the number of time intervals required is 7014=5{\displaystyle {\frac {70}{14}}=5}. , In most cases, you'll already have the answer in terms of years, seconds, or another convenient measurement.
If you measured the growth rate across a larger span of time, however, you may want to multiply to get your answer in terms of single units of time.
Example 1 (cont):
In this case, since we measured the growth across one year, each time interval is one year.
The island population doubles every 5 years.
Example 2:
The second, spider-infested island nearby is much less popular.
It also grew from a population of 20,000 to 22,800, but took 20 years to do it.
Assuming its growth is exponential, what is this population's doubling time? This island has a 14% growth rate over 20 years.
The "rule of 70" tells us it will also take 5 time intervals to double, but in this case each time interval is 20 years. (5 time intervals) x (20 years/time interval) = 100 years for the spider-infested island's population to double. -
Step 3: Divide 70 by the percentage growth rate.
-
Step 4: Convert your answer to the desired unit of time.
Detailed Guide
Doubling time is a concept used for quantities that grow exponentially.
Interest rates and the growth of a population are the most common examples used.
If the growth rate is less than about
0.15 per time interval, we can use this fast method for a good estimate.If the problem doesn't give you the growth rate, you can find it in decimal form using CurrentQuantity−PastQuantityPastQuantity{\displaystyle {\frac {CurrentQuantity-PastQuantity}{PastQuantity}}}.
Example 1:
The population of an island grows at an exponential rate.
From 2015 to 2016, the population increases from 20,000 to 22,800.
What is the population's growth rate? 22,800
- 20,000 = 2,800 new people. 2,800 ÷ 20,000 =
0.14, so the population is growing by
0.14 per year.
This is small enough that the estimate will be fairly accurate.
Most people find this more intuitive than the decimal fraction.
Example 1 (cont):
The island had a growth rate of
0.14, written as a decimal fraction.
This represents
0.141{\displaystyle {\frac {0.14}{1}}}.
Multiply the numerator and denominator by 100 to get
0.141x100100=14100={\displaystyle {\frac {0.14}{1}}x{\frac {100}{100}}={\frac {14}{100}}=} 14% per year. , The answer will be the number of time intervals it takes the quantity to double.
Make sure you express the growth rate as a percentage, not a decimal, or your answer will be off. (If you're curious why this "rule of 70" works, read the more detailed method below.) Example 1 (cont):
The growth rate was 14%, so the number of time intervals required is 7014=5{\displaystyle {\frac {70}{14}}=5}. , In most cases, you'll already have the answer in terms of years, seconds, or another convenient measurement.
If you measured the growth rate across a larger span of time, however, you may want to multiply to get your answer in terms of single units of time.
Example 1 (cont):
In this case, since we measured the growth across one year, each time interval is one year.
The island population doubles every 5 years.
Example 2:
The second, spider-infested island nearby is much less popular.
It also grew from a population of 20,000 to 22,800, but took 20 years to do it.
Assuming its growth is exponential, what is this population's doubling time? This island has a 14% growth rate over 20 years.
The "rule of 70" tells us it will also take 5 time intervals to double, but in this case each time interval is 20 years. (5 time intervals) x (20 years/time interval) = 100 years for the spider-infested island's population to double.
About the Author
Nicholas Campbell
Experienced content creator specializing in hobbies guides and tutorials.
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