Question $5$

Suppose we define $\backslash ($ y$=\backslash )$ the number of people in a small town after $\backslash ($ t $\backslash )$ years. Initially there are $500$ people in this small town. The population grows by $10\backslash \%$ per year, resulting in the ODE $\backslash (\backslash$frac$\{$d y$\}\{$d t$\}=0\mathrm{.}1$ y $\backslash ).$

After solving the ODE, determine at what time, $\backslash ($ t $\backslash ),$ the population is expected to double in size. State your answer as a value of time rounded to two decimal places.

NOTE: Keep your values exact until the very end. Then round your answer.

Choose the correct answer from the options below$\mathrm{.}4\mathrm{.}933\mathrm{.}935\mathrm{.}936\mathrm{.}932\mathrm{.}93$