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 · 3n = 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 · 37 = 1
Let s = the total number of students in school.