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In $2010$ , the population of a city was $240,000$ . From $2010$ to $2015$ , the population grew by $5.3\%$ . From $2015$ to $2020$ , it fell by $3.5\%$ . To the nearest whole number, by what percent did the city grow from $2010$ to $2020$ ?

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Percent of change: word problems

Full solution

Q. In

2010

, the population of a city was

240,000

. From

2010

to

2015

, the population grew by

5.3\%

. From

2015

to

2020

, it fell by

3.5\%

. To the nearest whole number, by what percent did the city grow from

2010

to

2020

?

Calculate Population $2015$ : Calculate the population in $2015$ after a $5.3\%$ increase from $2010$ . $\newline$ Population in $2010$ : $240,000$ $\newline$ Percentage increase from $2010$ to $2015$ : $5.3\%$ $\newline$ Population in $2015$ = Population in $2010$ + (Population in $2010$ $\times$ Percentage increase) $\newline$ Population in $2015$ = $240,000$ + ( $240,000$ $\times$ $0.053$ ) $\newline$ Population in $2015$ = $240,000$ + $12,720$ $\newline$ Population in $2015$ = $240,000$ $0$
Calculate Population $2020$ : Calculate the population in $2020$ after a $3.5\%$ decrease from $2015$ . $\newline$ Population in $2015$ : $252,720$ $\newline$ Percentage decrease from $2015$ to $2020$ : $3.5\%$ $\newline$ Population in $2020$ = Population in $2015$ - (Population in $2015$ $\times$ Percentage decrease) $\newline$ Population in $2020$ = $252,720$ - ( $252,720$ $\times$ $0.035$ ) $\newline$ Population in $2020$ = $252,720$ - $8,845.2$ $\newline$ Population in $2020$ = $252,720$ $0$
Round Population $2020$ : Round the population in $2020$ to the nearest whole number. $\newline$ Population in $2020$ (rounded) = $243,875$
Calculate Overall Percentage Change: Calculate the overall percentage change from $2010$ to $2020$ . $\newline$ Population in $2010$ : $240,000$ $\newline$ Population in $2020$ (rounded): $243,875$ $\newline$ Change in population $= \text{Population in 2020} - \text{Population in 2010}$ $\newline$ Change in population $= 243,875 - 240,000$ $\newline$ Change in population $= 3,875$ $\newline$ Percentage change $= (\text{Change in population} / \text{Population in 2010}) \times 100\%$ $\newline$ Percentage change $= (3,875 / 240,000) \times 100\%$ $\newline$ Percentage change $= 0.0161458333 \times 100\%$ $\newline$ Percentage change $= 1.61458333\%$
Round Percentage Change: Round the percentage change to the nearest whole number. $\newline$ Percentage change (rounded) = $2\%$

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