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The population of a city increases by
4% per year. If this year's population is
p, which expression represents next year's population?

1.004 p

1.04 p

4p

0.04 p

The population of a city increases by $4 \%$ per year. If this year's population is $p$ , which expression represents next year's population? $\newline$ $1.004 p$ $\newline$ $1.04 p$ $\newline$ $4 p$ $\newline$ $0.04 p$

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Write exponential functions: word problems

Full solution

Q. The population of a city increases by

4 \%

per year. If this year's population is

p

, which expression represents next year's population?

\newline

1.004 p

\newline

1.04 p

\newline

4 p

\newline

0.04 p

Rephrase Question: First, let's rephrase the ＂What expression represents the population of a city next year if it increases by $4\%$ from this year's population $p$ ?＂
Calculate Percentage Increase: To find next year's population, we need to increase this year's population by $4\%$ . An increase of $4\%$ means the population will be $100\%$ of the current population plus an additional $4\%$ . In terms of a decimal multiplier, this is $1$ (which represents the current $100\%$ ) plus $0.04$ (which represents the additional $4\%$ ).
Calculate Next Year's Population: To calculate the expression for next year's population, we add $1$ and $0.04$ to get $1.04$ . Therefore, the expression for next year's population is $1.04$ times this year's population, $p$ .
Final Expression: The correct expression that represents next year's population is $1.04 p$ . This means that the population will be $104\%$ of this year's population.

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