QIf the population of a town increased by 5% over the course of one year, and the total population at the end of the second year is 9975, then what was the population size at the beginning of the first year?
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Explanation
To find the population size at the beginning of the first year, we can use the formula:
Population at the beginning of the first year = (Total population at the end of the second year) / (1 + (percentage increase)) * (1 - (percentage increase))
Plugging in the values from the given information, we get:
Population at the beginning of the first year = 9975 / (1 + (5/100)) * (1 - (5/100))
Simplifying this expression, we get:
Population at the beginning of the first year = 9975 * (20/21) * (20/19)
Which simplifies to:
Population at the beginning of the first year = 10000
So the population at the beginning of the first year was 10000.
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