How to calculate the population growth using an exponential function

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 = 1.025n

Log1.025 2 = Log1.025(1.025)n

Log1.025 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.

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