A town's population is currently 6,595. If the population doubles every 29 years, what will the population be 145 years from now?
Understand the Problem
The question is asking for the future population of a town based on its current population, how often it doubles, and the time frame in years. We will solve this by calculating how many times the population doubles in the given time and then applying that growth factor to the current population.
Answer
The future population will be $210,240$.
Answer for screen readers
The future population of the town will be $210,240$.
Steps to Solve
- Calculate the number of doubling periods First, determine how many times the population will double in 145 years. You can find this by dividing the total years by the doubling time.
$$ \text{Number of doublings} = \frac{145 \text{ years}}{29 \text{ years/doubling}} $$
- Perform the division Now, perform the division to find the number of doublings.
$$ \text{Number of doublings} = \frac{145}{29} = 5 $$
- Calculate the future population To find the future population, multiply the current population by (2) raised to the power of the number of doublings.
$$ \text{Future Population} = 6595 \times 2^{5} $$
- Perform the multiplication Now, calculate (2^5) and then multiply it by the current population.
$$ 2^5 = 32 $$
So,
$$ \text{Future Population} = 6595 \times 32 $$
- Final calculation Now, perform the multiplication to find the future population.
$$ \text{Future Population} = 210,240 $$
The future population of the town will be $210,240$.
More Information
This calculation shows how exponential growth can significantly increase a population over time, demonstrating the impact of a relatively short doubling period.
Tips
- Forgets to divide total years by the doubling time to find the correct number of doublings.
- Incorrectly calculates the multiplication at the end.
- Confuses the growth factor by miscalculating (2^n).
AI-generated content may contain errors. Please verify critical information
