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 Question from hunter, a student: The population of a certain town in 1984 was 2900 people. The percent increase was 2.5% each year. What is the town's population in 2002?

Hi Hunter,

$2.5\%$ is $0.025$ so the increase in population from 1984 to 1985 would be $0.025 \times 2900.$ Hence the population in 1985 would be

${\bf 2900} + 0.025 \times {\bf 2900} = (1 + 0.025) \times {\bf 2900} = 1.025 \times 2900.$

The increase in population from 1985 to 1986 would then be $0.025 \times (1.025 \times 2900)$ so the population in 1986 would be

${\bf 1.025 \times 2900} + 0.025 \times {\bf (1.025 \times 2900)} = (1 + 0.025) \times \left[{\bf 1.025 \times 2900}\right] = 1.025 \times {\bf 1.025 \times 2900} = (1.025)^2 \times 2900$

What would be the population in 1987?

What would be the population in 2002?

Penny

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