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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?

p+0.04 p

0.04 p

1+0.04 p

4p

The population of a city increases by $4 \%$ per year. If this year's population is $p$ , which expression represents next year's population? $\newline$ $p+0.04 p$ $\newline$ $0.04 p$ $\newline$ $1+0.04 p$ $\newline$ $4 p$

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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

p+0.04 p

\newline

0.04 p

\newline

1+0.04 p

\newline

4 p

Define question prompt: Let's define the question_prompt: What expression represents next year's population if the current year's population is $p$ and it increases by $4\%$ per year?
Calculate increase: To find next year's population, we need to add the increase to the current population. The increase is $4\%$ of the current population, which is $0.04 \times p$ .
Expression for next year's population: The expression for next year's population is the current population plus the increase, which is $p + 0.04p$ .
Factor out $p$ : We can factor out $p$ from the expression to simplify it. This gives us $p(1 + 0.04)$ , which is the same as $1.04p$ .
Final expression: The correct expression that represents next year's population is therefore $1.04p$ , which is the current population plus $4\%$ of the current population.

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