If $$8500$ is invested at $12\mathrm{.}4\%$ compounded continuously, the future value $S$ at any time $t($in years$)$ is given by the following formula. $($Round your answers to two decimal places.$)$

$S=8500e^{0\mathrm{.}124t}$

$($a$)$ What is the amount after $18$ months?

$S=$$

$($b$)$ How long before the investment doubles?

$t=,yr$