suppose that there is a rumor going around your school that next all weekends will be extended to three days. Initally on day, 0, 10. students know thr rumor. suppose that each person who knows the rumor tell two more students the day after they hear about it. assume that no-one hears the rumor more than once. how many people will leam about the rumor....
To find out how many people will learn about the rumor, we can solve this problem using the concept of exponential growth. Let's break it down step by step:
1. On day 0, 10 students know the rumor. We start with this initial number.
2. On day 1, each of these 10 students tells two more students about the rumor. So, we multiply the initial number of students (10) by 2, resulting in 10 * 2 = 20 students knowing the rumor on day 1.
3. On day 2, each of the 20 students who heard the rumor on day 1 tells two more students. Again, we multiply the number of students from the previous day (20) by 2, resulting in 20 * 2 = 40 students knowing the rumor on day 2.
4. Following this pattern, we continue multiplying the number of students by 2 for each subsequent day.
Using this exponential growth formula, we can determine the number of students who will have heard the rumor on any given day.
In general, the formula is: number of students on day n = 10 * (2^n), where n represents the number of days after day 0.
For example, on day 3, the number of students would be: 10 * (2^3) = 10 * 8 = 80 students.
Therefore, to directly answer your question, on day 10 (ten days after day 0), the number of students who will have learned about the rumor would be: 10 * (2^10) = 10 * 1024 = 10,240 students.