A model for the number N of people in a college community who have heard a certain rumor is N= P(1-e^-0.15d)
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?
The number of people that hear a rumor in a college is modeled by N = P*(1 - e^(-0.15*d)) where P is the total number of students and d is the number of days that pass.
If the total number of students is 1000 and 450 people have to hear the rumor, the number of days that pass after which this happens is give by:
450 = 1000*(1 - e^(-0.15*d))
=> 1 - e^(-0.15*d) = 450/1000
=> e^(-0.15*d) = 1 - 450/1000
=> e^(-0.15*d) = 550/1000
Take the natural log of both the sides
= -0.15*d = ln(.55)
d = 3.98 days
The number of days after which 450 students hear the rumor is 3.98 or approximately 4 days.