A town has a population of 53,800 and shrinks at a rate of 2.5% every year. Which equation represents the town’s population after 3 years?
Question
A town has a population of 53,800 and shrinks at a rate of 2.5% every year. Which equation represents the town’s population after 3 years?
Solution
The equation that represents the town's population after 3 years is:
P = 53800 * (1 - 0.025)^3
Here's the step-by-step explanation:
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The initial population of the town is 53,800.
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The town shrinks at a rate of 2.5% every year. This can be represented as a decrease of 0.025 (since 2.5% = 0.025 when expressed as a decimal).
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The population after one year would be 53800 * (1 - 0.025), which represents a 2.5% decrease from the initial population.
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To find the population after 3 years, we raise the term (1 - 0.025) to the power of 3, because the population decreases by 2.5% each year for 3 years.
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Therefore, the equation P = 53800 * (1 - 0.025)^3 represents the town's population after 3 years.
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