A city's population is increasing at a rate of 2% per year.If this rate of growth remains the same and the population is 2 million in the year 2014, approximately how many people will there be after 20 years?
Question
A city's population is increasing at a rate of 2% per year.If this rate of growth remains the same and the population is 2 million in the year 2014, approximately how many people will there be after 20 years?
Solution
To solve this problem, we can use the formula for exponential growth, which is:
P = P0 * (1 + r)^t
where:
- P is the future population
- P0 is the initial population
- r is the rate of growth (expressed as a decimal)
- t is the time (in years)
Given in the problem, we have:
- P0 = 2,000,000 (the population in 2014)
- r = 0.02 (2% expressed as a decimal)
- t = 20 (the number of years)
Substituting these values into the formula, we get:
P = 2,000,000 * (1 + 0.02)^20
Calculating this gives:
P ≈ 2,000,000 * 1.485947
P ≈ 2,971,894
So, if the city's population continues to grow at a rate of 2% per year, there will be approximately 2,971,894 people after 20 years.
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