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The population of a city decreases by
3% per year. If this year's population is
p, which expression represents next year's population?

0.97 p

3p

0.997 p

0.03 p

The population of a city decreases by $3 \%$ per year. If this year's population is $p$ , which expression represents next year's population? $\newline$ $0.97 p$ $\newline$ $3 p$ $\newline$ $0.997 p$ $\newline$ $0.03 p$

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Exponential growth and decay: word problems

Full solution

Q. The population of a city decreases by

3 \%

per year. If this year's population is

p

, which expression represents next year's population?

\newline

0.97 p

\newline

3 p

\newline

0.997 p

\newline

0.03 p

Understand Population Decrease: Understand the percentage decrease in the population. $\newline$ The population decreases by $3\%$ each year. This means that next year's population will be $100\% - 3\% = 97\%$ of this year's population.
Convert Percentage to Decimal: Convert the percentage to a decimal to use in calculations. $\newline$ To convert a percentage to a decimal, divide by $100$ . Therefore, $97\%$ becomes $97/100$ or $0.97$ .
Write Next Year's Expression: Write the expression for next year's population. If this year's population is $p$ , then next year's population will be $0.97 \times p$ , because the population retains $97\%$ of its size.

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