Question

A city has a population of 220,000 people. Suppose that each year the population grows by 8.5%. What will the population be after 15 years? Round to the nearest whole number.

Answer 1

`\bf \textit{Amount of Population Growth} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &220000\\ r=rate\to 8.5\%\to (8.5)/(100)\dotfill &0.085\\ t=\textit{elapsed time}\dotfill &15\\ \end{cases} \\\\\\ A=220000e^(0.085\cdot 15)\implies A=220000e^(1.275)\implies \stackrel{\textit{rounded up}}{A=787314}`

without rounding is about 787314.31, which means 787314 people plus 0.31 of another, we can only get 0.31 if we saw off one person, which is not happening, thus the rounding.