What was the approximate percent change, rounded to the nearest integer if required, in the per capita gross domestic product of the city from 2000 to \(2015 ?\)

Question

The population of City \(\mathrm{X}\) increased from 2 million in the year 2000 to \(2.5\) million in 2015 and the gross domestic product of the city in 2000 was \(\frac{3}{8}\) less than that in 2015 . What was the approximate percent change, rounded to the nearest integer if required, in the per capita gross domestic product of the city from 2000 to \(2015 ?\)

Answer 1

We know that 'the gross domestic product of the city in 2000 was \(\frac{3}{8}\) less than that in 2015 ,'so let's assume that the GDP in 2015 was 800 ; thus, the GDP in the year \(2000=800-\frac{3}{8} \times 800=500\).

We assumed a seemingly puzzling number '800' for the GDP in 2015 since we find that in the denominator of the fraction \(\frac{3}{8}\), we have to deal with ' 8, ' and ' 800 ' is a multiple of ' 8 ' - easy to deal with.
We know that the population year \(2000=2 \mathrm{M}\) and that in \(2015=2.5 \mathrm{M}\)
Thus,
Per capita GDP in \(2000=\frac{\text { GDP }}{\text { population }}=\frac{500}{2 \mathrm{M}}=\frac{250}{\mathrm{M}}\) and
Per capita GDP in \(2005=\frac{\text { GDP }}{\text { population }}=\frac{800}{2.5 \mathrm{M}}=\frac{8000}{25 \mathrm{M}}=\frac{320}{\mathrm{M}}\)
Thus,
\[
\begin{aligned}
& \text { Change in Per Capita GDP over 2000-2015 }=\frac{\text { (Per Capita GDP in 2015)-(Per Capita GDP in 2000) }}{\text { (Per Capita GDP in 2000) }} \times 100 \% \\
& =\frac{\frac{320}{\mathrm{M}}-\frac{250}{\mathrm{M}}}{\frac{250}{\mathrm{M}}} \times 100 \% \\
& =\frac{70}{250} \times 100 \% \text { (M gets cancelled) } \\
& =28 \%
\end{aligned}
\]