each of the 15 student council members of Blakemore Elementary School is responsable for telling exactly 2 other students about the upcoming school pep assembly. Each of those 2 is then responsable for telling 2 other students. It takes 15 minutes for each round of stundents to be told. How many minutes will take for 1,000 students to recive the information about the pep assembly ?
end of round1 -- 30 students -- 15 minutes
round2 -- 60 -- 30 min
round3 -- 120 -- 45
round4 -- 240 -- 60
round5 -- 480 -- 75
ruond6 -- 960 -- 90
round7 --1920 -- 105
what do you think?
ty
To find out how many minutes it will take for 1,000 students to receive the information about the pep assembly, we need to consider the number of rounds it takes for the information to reach all the students.
Initially, the 15 student council members tell 2 other students each, so that's a total of 15*2 = 30 students who have been informed in the first round.
In the second round, each of the 30 students tells 2 more students. So in the second round, 30*2 = 60 additional students receive the information. In total, there are now 30 (first round) + 60 (second round) = 90 students who know about the pep assembly.
In each subsequent round, the number of students who receive the information doubles. So in the third round, 60*2 = 120 students get informed, resulting in a total of 90 (previous rounds) + 120 (third round) = 210 students who know about the pep assembly.
We can observe a pattern here. In each round, the number of students reached is doubled. So, in general, the number of students reached in a particular round is given by 30*(2^(round-1)).
To find out how many rounds it takes to reach 1,000 students, we need to solve the following equation: 30*(2^(round-1)) = 1,000.
Let's calculate the value of round:
2^(round-1) = 1000/30
2^(round-1) = 33.33 (approximately)
To solve for round, we can take the logarithm base 2 of both sides:
log2(2^(round-1)) = log2(33.33)
(round-1) = log2(33.33)
Using a calculator, log2(33.33) is approximately 5.04.
So, round - 1 = 5.04.
Adding 1 to both sides, we get round = 6.04.
Since round represents the number of rounds it takes for everyone to be informed, we'll round up to the nearest whole number, giving us round = 7.
Therefore, it will take 7 rounds for 1,000 students to receive the information about the pep assembly.
Now, since each round takes 15 minutes, the time it will take for 1,000 students to receive the information is 7 rounds * 15 minutes per round = 105 minutes.