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The population of a city decreases by
2.2% per year. If this year's population is 305,000 , what will next year's population be, to the nearest individual?
Answer:

The population of a city decreases by $2.2 \%$ per year. If this year's population is $305$ , $000$ , what will next year's population be, to the nearest individual? $\newline$ Answer:

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Exponential growth and decay: word problems

Full solution

Q. The population of a city decreases by

2.2 \%

per year. If this year's population is

305

,

000

, what will next year's population be, to the nearest individual?

\newline

Answer:

Population decrease explanation: Understand the percentage decrease in population. The population decreases by $2.2\%$ each year. This means that for every $100$ individuals, $2.2$ individuals leave the population each year.
Calculate decrease: Calculate the number of individuals that represent the $2.2\%$ decrease. $\newline$ To find out how many individuals $2.2\%$ represents, we multiply the current population by the percentage decrease (expressed as a decimal). $\newline$ $2.2\%$ as a decimal is $0.022$ . $\newline$ So, the calculation is $305,000 \times 0.022$ .
Perform calculation: Perform the calculation from Step $2$ . $\newline$ $305,000 \times 0.022 = 6,710$ $\newline$ This means that $6,710$ individuals represent the $2.2\%$ decrease in the population.
Find next year's population: Subtract the decrease from the current population to find next year's population. $\newline$ To find next year's population, we subtract the number of individuals that left $6,710$ from the current population $305,000$ . $\newline$ $305,000 - 6,710 = 298,290$
Round to nearest whole number: Round the result to the nearest individual. $\newline$ Since we cannot have a fraction of an individual, we round the number to the nearest whole number. $\newline$ $298,290$ is already a whole number, so no rounding is necessary.

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