A person begins a fake news story by telling it to five people. Call this Generation 1. Each of those five people tells the story to five different people. Call this Generation 2. Now each of the people in Generation 2 tells the story to five different people. This is Generation 3. For each of the following parts, assume no one tells the story to a person who has already heard the story and that once a person tells the story to five other people, that person does not tell the story again.
(a)
How many people will hear the story in Generation 1?
5
Correct: Your answer is correct.
(b)
How many people will hear the story in Generation 2?
25
Correct: Your answer is correct.
(c)
How many people will hear the story in Generation 3?
125
Correct: Your answer is correct.
(d)
What is the percentage increase in the number of people who will hear the story from one Generation to another? show your work
To calculate the percentage increase in the number of people who will hear the story from one Generation to another, we can use the following formula:
Percentage Increase = ((Number of People in Later Generation - Number of People in Earlier Generation) / Number of People in Earlier Generation) * 100
For the increase from Generation 1 to Generation 2:
((25 - 5) / 5) * 100 = (20 / 5) * 100 = 4 * 100 = 400%
For the increase from Generation 2 to Generation 3:
((125 - 25) / 25) * 100 = (100 / 25) * 100 = 4 * 100 = 400%
Therefore, the percentage increase in the number of people who will hear the story from one Generation to another is 400% for both transitions.