Use the average growth rate between 1970 and 2000, which was about 0.5%, to find the approximate doubling time and to predict the population in 2050 of a growing
suburban town (based on a 2000 population of 100,000). Round to the nearest year and person.
To find the approximate doubling time, we can use the formula for exponential growth:
Doubling Time = ln(2) / (r * ln(1 + r))
where r is the growth rate as a decimal.
Given that the growth rate is 0.5%, we can convert it to decimal form: r = 0.5% = 0.005.
Now we can calculate the doubling time:
Doubling Time = ln(2) / (0.005 * ln(1 + 0.005))
Doubling Time ≈ 138.57
So, the approximate doubling time is 138.57 years.
To predict the population in 2050, we need to determine the number of doubling times that will pass between 2000 and 2050. Since 50 years will have passed, we can calculate how many doubling times fit into that period:
Number of Doubling Times = 50 / Doubling Time
Number of Doubling Times ≈ 50 / 138.57
Number of Doubling Times ≈ 0.3608
Now we can use the formula for exponential growth to find the projected population in 2050:
Projected Population in 2050 = Initial Population * (1 + r)^(Number of Doubling Times)
Projected Population in 2050 ≈ 100,000 * (1 + 0.005)^0.3608
Projected Population in 2050 ≈ 100,000 * 1.002056
Projected Population in 2050 ≈ 100,205.6
Rounding to the nearest person, the projected population of the suburban town in 2050 will be approximately 100,206 people.