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Answer :
Final answer:
A population with a doubling time of 25 years will grow by a factor of 2 in 25 years, by a factor of 4 in 50 years, and by a factor of 16 in 100 years, based on the exponential growth rule.
Explanation:
If a population has a doubling time of 25 years, by what factor will it grow in various timeframes? Let's calculate this using the rule of exponential growth.
In 25 years, the factor by which the population will grow is 2, because the definition of doubling time implies that the population doubles every 25 years.
In 50 years, which is two doubling periods, the population will grow by a factor of 2^2 (2 raised to the power of 2), which is 4.
In 100 years, which is four doubling periods, the population growth factor will be 2^4 (2 raised to the power of 4), which equals 16.
Thus:
- After 25 years, growth factor = 2
- After 50 years, growth factor = 4
- After 100 years, growth factor = 16
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