### Home > CC4 > Chapter 11 > Lesson 11.1.2 > Problem 11-18

A rumor about the school dance is being spread throughout a school. It began at 8 a.m. this morning, and each hour the fraction of the students that know the rumor triples. The principal does not know what fraction of students started the rumor. Homework Help ✎

What is the multiplier for the geometric sequence in this situation?

By 3 p.m. this afternoon, every student has heard the rumor. What fraction of students had heard the rumor at 2 p.m.?

Let

*a*represent the unknown fraction of the student population that started the rumor. Write an equation for a geometric sequence that represents the fraction of students that have heard the rumor after*n*hours.Use the fact that the every student has heard the rumor by 3 p.m. and your equation to determine the fraction of the student population that started the rumor.

If a group of 3 students started the rumor initially, how many students are in the school?

How do you triple something?

Between 2 p.m. and 3 p.m., the number of people who had heard the rumor tripled so that the whole student body knows.

If the whole student body is 1, what fraction times 3 equals 1? That is, ? · 3 = 1?

*a* · 3* ^{n}* =

*y*

Use the equation from part (c) where *n* is the number of hours that have passed between 8 a.m. and 3 p.m. and *y* is 1.

Solve the equation for *a*: *a* · 3^{7} = 1

Let *s* = the total number of students in school.