Question

Abbie made a video of herself singing and posted it online. After one hour, the video has 100 views. After two hours the video has 150 views 50% more than there were after one hour. After three hours, the video has 225 views. If this pattern continues, approximately how many hours will it take for Abbie's video to reach 1, 000 views?

Answer 1

Abbie's video views increase by 50% each hour. Starting from 100 views, a repeated application of the 50% increase shows that her video will reach 1,000 views after approximately 7 hours.

Step-by-step explanation:

The student is asking about a pattern of increases in video views over time and wondering how long it will take to reach a certain number of views. To solve this, we examine the pattern established in the first three hours: from 100 views to 150 views (a 50% increase), and then to 225 views (another 50% increase from 150). This sequence suggests that the number of views increases by 50% each hour.

To find when the video will reach 1,000 views, we can use the geometric sequence formula or repeatedly apply the 50% growth rate until we exceed 1,000 views. Let's calculate step-by-step:

• After 1 hour: 100 views
• After 2 hours: 150 views (50% more than after 1 hour)
• After 3 hours: 225 views (50% more than after 2 hours)

If we continue this pattern:

• After 4 hours: 225 views + (225 views * 0.5) = 337.5 views
• After 5 hours: 337.5 views + (337.5 views * 0.5) = 506.25 views
• After 6 hours: 506.25 views + (506.25 views * 0.5) = 759.375 views
• After 7 hours: 759.375 views + (759.375 views * 0.5) = 1139.0625 views

Therefore, Abbie's video will reach 1,000 views after approximately 7 hours.

Answer 2

It will take approximately 7 hours for Abbie's video to reach 1,000 views following the pattern of a 50% increase in views each hour.

Step-by-step explanation:

The student's question is asking how long it will take for Abbie's video to reach 1,000 views given a specific viewing pattern. Looking at the information provided, after one hour there are 100 views, and after two hours, the video has 150 views, indicating an increase of 50%. After three hours, the video reaches 225 views, which is again a 50% increase from the previous hour. This pattern suggests that the number of views is increasing by 50% each hour.

To find out when the video will reach 1,000 views, we can use the geometric sequence formula or observe the pattern of growth:

• 1st hour: 100 views
• 2nd hour: 150 views (100 + 50)
• 3rd hour: 225 views (150 + 75)

Continuing this pattern:

• 4th hour: 337.5 views (225 + 112.5)
• 5th hour: 506.25 views (337.5 + 168.75)
• 6th hour: 759.375 views (506.25 + 253.125)
• 7th hour: 1139.0625 views (759.375 + 379.6875)

By the 7th hour, Abbie's video will have approximately 1139 views, surpassing the 1,000 view target. Therefore, it will take approximately 7 hours for Abbie's video to reach 1,000 views.