QuestionA rumour is being spread in a community that the mayor is going to retire before the next election. Initially, 6 people were told the rumour and each of these people told 6 others the following day. Each of the 6 people told by the initial people told 6 others the day after they were told. If this process keeps up, how many people will be told the rumour on the eighth day? a. people b. people c. 1679616 people d. 10077696 people
Studdy Solution
STEP 1
1. Initially, 6 people know the rumor.
2. Each person who knows the rumor tells 6 others the next day.
3. This process continues without any interruption or change in pattern.
4. We are tasked with finding the number of people who will be told the rumor on the eighth day.
STEP 2
1. Identify the pattern of rumor spreading.
2. Define the mathematical model.
3. Calculate the number of people told on the eighth day.
STEP 3
Identify the pattern of rumor spreading.
Each day, every person who knows the rumor tells 6 new people. This forms a geometric progression where the number of people told each day is a power of 6.
STEP 4
Define the mathematical model.
The number of people told on the -th day can be represented as:
STEP 5
Calculate the number of people told on the eighth day.
Substitute into the model:
Calculate :
Thus, the number of people told the rumor on the eighth day is:
Was this helpful?
