Chapter 4.4, Problem 126AYU

Spreading of Rumors A model for the number $N$ of people in a college community who have heard a certain rumor is

$N\left(\text{d }\right)=\text{ P}\left(1-e^{-0.15d}\right)$

where $P$ is the total population of the community and $d$ is the number of days that have elapsed since the rumor began. In a community of $1000$ students, how many days will elapse before $450$ students have heard the rumor?