Question

On the first day it was posted online, a music video got 510 views. The number of views that the video got each day increased by 20% per day. How many total views did the video get over the course of the first 20 days, to the nearest whole number?

Answer 1

The video's daily views increase by 20%, starting with 510 views on day 1. By day 20, it accumulates around 19,552 views, with a total of approximately 114,763 views over the 20-day period.

1. Define the growth rate:

The video starts with 510 views on day 1.

Each day, the number of views increases by 20%.

2. Calculate the daily increase:

20% of 510 views is (20/100) * 510 = 102 views.

3. Create a formula for daily views:

On day 2, the number of views will be 510 + 102 = 612.

In general, on day n, the number of views will be 510 * (1 + 20/100)^n.

4. Calculate the total views on day 20:

Using the formula above, on day 20, the number of views will be 510 * (1 + 20/100)^20 ≈ 19,552.

5. Calculate the total views for 20 days (cumulative total):

To find the total views for all 20 days, we need to sum the daily views for each day. This can be done with a spreadsheet or by using a geometric series formula. The sum for 20 days is approximately 114,763.

Therefore:

On day 20, the video will have approximately 19,552 views.

Over the first 20 days, the video will have a cumulative total of approximately 114,763 views.

Answer 2

19,552 views on day 20, 114,763 views cumulative total for 20 days.

Explanation:

The decimal equivalent to "increased by 20% per day" would be (510)*(1.20)/day, if we started with 510 views as day 0. Day 1 would be (510)*(1.20) = 612 views.

If we have n successively days, the equation would read (510)(1.20)^n.

This means that after, lets say, 3 days, the calculation would be (510)*(1.20)^3, or 881 views.

On day 20, the calculation is (510)*(1.2)^20, or 19,552 views.

But the question asks "How many total views did the video get over the course of the first 20 days . . ?" This seems to be asking the sum of the first 20 days, which is easy if you use a spreadsheet. But if you read the question to mean what are the total views on day 20, the answer would be 19,552 views.

If you read the question as asking for the total sum of views over 30 days, the answer is 114,763. Quick: what does that amount to at $0.05 per view.