The population of a town with an initial population of 60,000 grows at a rate of 2.5% per year. What is population in 5 years? In 10 years? How many years will it take it to double from 60,000 to 120,000?
Solution
The formula to use is B = A (1 + r)^{n}
B = population after growth
A = population before growth
r = 2.5% = 0.025
n = number of years
Population in 5 years
B = 60000 (1 + 0.025)^{5}
B = 60000 (1.025)^{5}
B = 60000 x 1.13140821289
B = 67884.4927734
Population in 10 years
B = 60000 (1 + 0.025)^{10}
B = 60000 (1.025)^{10}
B = 60000 x 1.2800845442
B = 76805.0726518
When will the population double?
120000 = 60000 (1 + 0.025)^{n}
120000/60000 = 60000/60000(1 + 0.025)^{n}
2 = 1.025^{n}
Log_{1.025} 2 = Log_{1.025}(1.025)^{n}
Log_{1.025} 2 = n
n = ln 2 / ln (1.025)
n = 0.69314718056 / 0.02469261259
n = 28.0710346262
The population will double in a little more than 28 years.
Sep 27, 22 08:34 AM