Because of an economic downturn, the population of a certain urban area declines at a rate of 1.5% per year. Initially, the population is 165000. To the nearest person, what is the population after 5 years?
Question
Because of an economic downturn, the population of a certain urban area declines at a rate of 1.5% per year. Initially, the population is 165000. To the nearest person, what is the population after 5 years?
Solution
To solve this problem, we need to understand that a decline of 1.5% per year means that each year, the population is 98.5% (100% - 1.5%) of what it was the previous year.
Here are the steps to solve this problem:
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Convert the percentage to a decimal: 1.5% = 0.015. So, 98.5% = 0.985.
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We know that the population declines for 5 years. So, we need to multiply the initial population by 0.985 five times. In mathematical terms, this is equivalent to raising 0.985 to the power of 5.
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Calculate the population after 5 years: 165000 * (0.985^5).
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Round the result to the nearest person.
Let's do the calculation:
165000 * (0.985^5) = 155807.79
When we round this to the nearest person, we get 155808.
So, the population of the urban area after 5 years is approximately 155808.
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