billions$)$ as a function of time $t($in years$),$ with $t=0$ corresponding to the beginning of $1990.$

$($a$)$ Find the function $Q(t)$ that expresses the world population $($in billions$)$ as a function of time $t($in years$).$

$Q(t)=$

$($b$)$ If the world population continues to grow at the rate of approximately $2\frac{\%}{?}$ year, find the length of time $t_4($in yr$)$ required for the world population to quadruple in size. $($Round your answer to two decimal places.$)$

$t_4=$ yr

$($c$)$ Using the time $t_4$ found in part $($a$),$ what would be the world population $($in billions of people$)$ if the growth rate were reduced to $1\mathrm{.}2\frac{\%}{y}$ r$?($Round your answer to two decimal places.$)$

$$ billion