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 175000. To the nearest person, what is the population after 6 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 175000. To the nearest person, what is the population after 6 years?
Solution
To solve this problem, we need to understand that a 1.5% decline 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 6 years. So, we need to multiply the initial population by 0.985 six times. In mathematical terms, we raise 0.985 to the power of 6.
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Multiply the initial population by the result from step 2.
Let's do the calculations:
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0.985 raised to the power of 6 is approximately 0.914.
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Multiply the initial population by this result: 175000 * 0.914 = 159950.
So, to the nearest person, the population after 6 years is approximately 159950.
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