A town has a population of 10000 and grows at 5% every year. What will be the population after 5 years, to the nearest whole number?
Question
A town has a population of 10000 and grows at 5% every year. What will be the population after 5 years, to the nearest whole number?
Solution
To solve this problem, we can use the formula for compound interest, which is also applicable to population growth. The formula is:
P = P0 * (1 + r)^n
where:
- P is the future population
- P0 is the initial population
- r is the growth rate (in decimal form)
- n is the number of years
Given in the problem:
- P0 = 10000 (initial population)
- r = 5/100 = 0.05 (growth rate in decimal form)
- n = 5 (number of years)
Substituting these values into the formula, we get:
P = 10000 * (1 + 0.05)^5
Calculating the value, we get:
P = 10000 * (1.05)^5 P = 10000 * 1.2762815625 P = 12762.815625
Rounding to the nearest whole number, the population after 5 years will be approximately 12763.
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