In $2014,$ the world's population reached $7\mathrm{.}17$ billion ${?}^1$ and was increasing at a rate of $1\mathrm{.}1\%$ per year. Assume that this growth rate remains constant. $($In fact, the growth rate has decreased since $2008.)$

$($a$)$ Enter a formula for the world population, $P,($in billions$)$ as a function of the number of years, $t,$ since $2014.$

$P(t)=$

$$

$($b$)$ Estimate the population of the world in the year $2036.$ NOTE: Round your answer to two decimal places.

$P=$ billion people