Use the current annual growth ate, which is about 3.5%, to find the approximate doubling time and to predict the population in 2050 of a groying suburban town (based on a 2000 population of 100,000). Round to the nearest year and person.
A. 22 years; 2050 population = 800,000
B. 30 years; 2050 population = 400,000
C. 15 years; 2050 population = 282,843
D. 20 years; 2050 population = 565,685
The population of any area, whether it’s a bustling city or a quiet suburban town, can grow over time. Using the annual growth rate, we can make predictions about how long it’ll take for a population to double and what it might be at a future date. Let’s examine a hypothetical suburban town that had a population of 100,000 in the year 2000, with an annual growth rate of 3.5%.
Understanding the Doubling Time: The doubling time of a population is the number of years it would take for that population to double, given a constant growth rate. There’s a simple formula that relates the doubling time to the growth rate: Doubling Time(T)=70Growth Rate (r)Doubling Time(T)=Growth Rate (r)70 Where r is in percentage.
Using the given growth rate of 3.5%, the doubling time TT is: T=703.5=20 yearsT=3.570=20 years
Predicting the Population in 2050: Starting from the year 2000 with a population of 100,000, after 20 years (by 2020), the population would have doubled to 200,000. After another 20 years (by 2040), it would double again to 400,000.
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However, by 2050, it’s only been an additional 10 years from 2040. This isn’t enough time for the population to double again, but we can use the growth rate to estimate the increase. In 10 years, at a growth rate of 3.5%, the population would grow by about 41% (because 3.5% compounded annually for 10 years gives approximately 41%).
41% of 400,000 is 164,000.
Adding this to the 400,000 from 2040, we get a total predicted population of 564,000 by 2050.
The Verdict:
• A. 22 years; 2050 population = 800,000 – This overestimates both the doubling time and the 2050 population.
• B. 30 years; 2050 population = 400,000 – This also overestimates the doubling time, and while the 2050 population is close, it’s a little low.
C. 15 years; 2050 population = 282,843 – This underestimates the doubling time and the 2050 population.
• D. 20 years; 2050 population = 565,685 – This choice is the closest to our calculations, with a doubling time of 20 years and a 2050 population of approximately 564,000.
Therefore, based on our analysis and the options provided, the most accurate answer is 20 years for the doubling time and a predicted population of 565,685 by 2050.
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