A city's population is currently 67,900. If the population doubles every 21 years, what will the population be 84 years from now?
Understand the Problem
The question is asking us to calculate the future population of a city based on its current population and a doubling rate. We need to determine how many doubling periods occur within 84 years and then apply that to the initial population.
Answer
1086400
Answer for screen readers
1086400
Steps to Solve
- Calculate the number of doubling periods
To find out how many times the population doubles in 84 years, we divide the total time (84 years) by the doubling time (21 years):
$ \text{Number of doubling periods} = \frac{84}{21} = 4 $
- Calculate the future population
The population doubles 4 times. This means we multiply the current population by 2 four times, or equivalently, multiply by $2^4$:
$ \text{Future population} = \text{Current population} \times 2^{\text{Number of doubling periods}} $
$ \text{Future population} = 67900 \times 2^4 $ $ \text{Future population} = 67900 \times 16 $ $ \text{Future population} = 1086400 $
1086400
More Information
The population of the city after 84 years will be 1,086,400 people, given the current population of 67,900 and a doubling time of 21 years.
Tips
A common mistake would be to multiply the current population by the number of doubling periods (4) instead of raising 2 to the power of the number of doubling periods. Another mistake could be an arithmetic error in the final multiplication step.
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