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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?

p-0.03

1p-0.03 p

3p
0.97

The population of a city decreases by $3 \%$ per year. If this year's population is $p$ , which expression represents next year's population? $\newline$ $p-0.03$ $\newline$ $1 p-0.03 p$ $\newline$ $3 p$ $\newline$ $0$ . $97$

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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

p-0.03

\newline

1 p-0.03 p

\newline

3 p

\newline

0

.

97

Identify percentage decrease: The question prompt is: ＂What expression represents next year's population if the current population is $p$ and it decreases by $3\%$ per year?＂
Convert to decimal: Identify the percentage decrease in the population. $\newline$ The population decreases by $3\%$ each year.
Calculate decrease: Convert the percentage decrease to a decimal. $\newline$ $3\%$ as a decimal is $0.03$ .
Subtract from current population: Calculate the decrease in population. $\newline$ The decrease in population is $3\%$ of $p$ , which is $0.03 \times p$ .
Simplify expression: Subtract the decrease from the current population to find next year's population. $\newline$ Next year's population is $p - (0.03 \times p)$ .
Simplify expression: Subtract the decrease from the current population to find next year's population. $\newline$ Next year's population is $p - (0.03 \times p)$ . Simplify the expression. $\newline$ Next year's population is $p - 0.03p$ , which simplifies to $0.97p$ .

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