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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?

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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:

  1. Convert the percentage to a decimal: 1.5% = 0.015. So, 98.5% = 0.985.

  2. 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.

  3. Multiply the initial population by the result from step 2.

Let's do the calculations:

  1. 0.985 raised to the power of 6 is approximately 0.914.

  2. Multiply the initial population by this result: 175000 * 0.914 = 159950.

So, to the nearest person, the population after 6 years is approximately 159950.

This problem has been solved

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