Question Video: Creating Exponential Expressions in One Variable Mathematics

The population of a small town decreases by 1/10 every year. Today, the population is 5000. Write an expression for the population in 𝑡 years. (Hint: by what do you multiply to produce a decrease of 1/10?)

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Video Transcript

The population of a small town decreases by one-tenth every year. Today, the population is 5000. Write an expression for the population in 𝑡 years. Hint: by what do you multiply to produce a decrease of one-tenth?

Let’s first convert one-tenth into a percentage or one-tenth is equal to 10 percent. This means that we have a 10 percent decrease. As the population is decreasing by 10 percent each year, the new population will be 90 percent of the previous year. 100 minus 10 equals 90. This means that our multiplier will be 0.9 as 90 percent is the same as 0.9.

After one year, the population would be 5000 multiplied by 0.9. After two years, the new population would be 5000 multiplied by 0.9 squared. This means that after 𝑡 years, an expression for the population would be 5000 multiplied by 0.9 to the power of 𝑡. 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.

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