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The population of a small town decreases by one-tenth every year.
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Today, the population is 5000.
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Write an expression for the population in 𝑡 years.
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Hint: by what do you multiply to produce a decrease of one-tenth?
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Let’s first convert one-tenth into a percentage or one-tenth is equal to 10 percent.
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This means that we have a 10 percent decrease.
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As the population is decreasing by 10 percent each year, the new population will be 90 percent of the previous year.
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100 minus 10 equals 90.
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This means that our multiplier will be 0.9 as 90 percent is the same as 0.9.
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After one year, the population would be 5000 multiplied by 0.9.
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After two years, the new population would be 5000 multiplied by 0.9 squared.
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This means that after 𝑡 years, an expression for the population would be 5000 multiplied by 0.9 to the power of 𝑡.
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This expression could be used to calculate the population at any time in the future assuming that it continues to decrease by one-tenth every year.