A video is posted on a hosting site (like YouTube) and gets 4 views in the first hour. Each of these 4 viewers share the video with 4 of their contacts (who also view the video) and at the end of the second hour the video has a total of 4 + 4(4) = 20 views. Each of the new 16 viewers share the video with 4 of their contacts (who also view the video) and at the end of the third hour the video has a total of 20 + 4(16) = 84 views. This pattern continues such that every hour the video accumulates an additional four times the number of views that it received in the previous hour. 1. How many views will the video have by the end of the 4th, 5th and 6th hour? 2. Define a linear homogenous recurrence relation for the number of views, an, at the end of the nth hour and do not forget to specify the initial conditions. Hint: express it in terms of the 2 previous terms. 3. Find a solution to the recurrence relation with the form an =α1rn+α2rn. 4. How many views will the video have by the end of the 12th hour using the closed-form solution that you obtained in #3.
A video is posted on a hosting site (like YouTube) and gets 4 views in the first hour. Each of these 4 viewers share the video with 4 of their contacts (who also view the video) and at the end of the second hour the video has a total of 4 + 4(4) = 20 views. Each of the new 16 viewers share the video with 4 of their contacts (who also view the video) and at the end of the third hour the video has a total of 20 + 4(16) = 84 views. This pattern continues such that every hour the video accumulates an additional four times the number of views that it received in the previous hour.
1. How many views will the video have by the end of the 4th, 5th and 6th hour?
2. Define a linear homogenous recurrence relation for the number of views, an, at the end of the nth hour and do not forget to specify the initial conditions. Hint: express it in terms of the 2 previous terms.
3. Find a solution to the recurrence relation with the form an =α1rn+α2rn.
4. How many views will the video have by the end of the 12th hour using the closed-form solution that you obtained in #3.
Step by step
Solved in 2 steps
