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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% 4 \% per year. If this year's population is p p , which expression represents next year's population?\newline1+0.04 1+0.04 \newline4p 4 p \newline1+0.04p 1+0.04 p \newline1.04p 1.04 p

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Q. The population of a city increases by 4% 4 \% per year. If this year's population is p p , which expression represents next year's population?\newline1+0.04 1+0.04 \newline4p 4 p \newline1+0.04p 1+0.04 p \newline1.04p 1.04 p
  1. Identify Population and Increase: Identify the current population and the percentage increase.\newlineThe current population is given as pp, and the increase is 4%4\% per year.
  2. Convert Percentage to Decimal: Convert the percentage increase to a decimal to use in calculations.\newline4%4\% as a decimal is 0.040.04.
  3. Calculate Additional Population: Calculate the additional population for next year due to the increase.\newlineThe additional population is 4%4\% of the current population, which is 0.04×p0.04 \times p.
  4. Find Next Year's Population: Add the additional population to the current population to find next year's population.\newlineNext year's population is pp (current population) plus 0.04×p0.04 \times p (increase), which is p+0.04×pp + 0.04 \times p.
  5. Simplify Expression: Simplify the expression for next year's population. Combine like terms to get the expression for next year's population: 1×p+0.04×p=(1+0.04)×p=1.04×p1 \times p + 0.04 \times p = (1 + 0.04) \times p = 1.04 \times p.

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