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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+0.04

4p

1+0.04 p

1.04 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? $\newline$ $1+0.04$ $\newline$ $4 p$ $\newline$ $1+0.04 p$ $\newline$ $1.04 p$

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Exponential growth and decay: 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+0.04

\newline

4 p

\newline

1+0.04 p

\newline

1.04 p

Identify Population and Increase: Identify the current population and the percentage increase. $\newline$ The current population is given as $p$ , and the increase is $4\%$ per year.
Convert Percentage to Decimal: Convert the percentage increase to a decimal to use in calculations. $\newline$ $4\%$ as a decimal is $0.04$ .
Calculate Additional Population: Calculate the additional population for next year due to the increase. $\newline$ The additional population is $4\%$ of the current population, which is $0.04 \times p$ .
Find Next Year's Population: Add the additional population to the current population to find next year's population. $\newline$ Next year's population is $p$ (current population) plus $0.04 \times p$ (increase), which is $p + 0.04 \times p$ .
Simplify Expression: Simplify the expression for next year's population. Combine like terms to get the expression for next year's population: $1 \times p + 0.04 \times p = (1 + 0.04) \times p = 1.04 \times p$ .

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