Eitan posted a video on the internet which only received approximately 100 views per day for the first 365 days after it was posted. However, on the 366^("th ") day, Eitan's video began to receive a greater following: the total number of views grew at a rate of 25% per day. Compared to the number of views Eitan's video received in the first 365 days, how many more views did his video receive in the 7 -day period after the first 365 days? Choose 1 answer: A) 36,500 B 101,000 C) 138,000 D) 174,000

Question

Eitan posted a video on the internet which only received approximately 100 views per day for the first 365 days after it was posted. However, on the  366^("th ") day, Eitan's video began to receive a greater following: the total number of views grew at a rate of  25% per day. Compared to the number of views Eitan's video received in the first 365 days, how many more views did his video receive in the 7 -day period after the first 365 days? Choose 1 answer: A) 36,500 B 101,000 C) 138,000 D) 174,000

Bytelearn · Accepted Answer

Calculate Total Views: Calculate the total number of views for the first 365 days. Since the video received approximately 100 views per day for the first 365 days, we multiply the number of views per day by the number of days. 100 views/day * 365 days = 36,500 viewsCalculate Views on 366th Day: Calculate the number of views on the 366th day. On the 366th day, the video starts to receive 25% more views than the previous day's 100 views. 25% of 100 views = 0.25 * 100 views = 25 views So, on the 366th day, the video received 100 views + 25 views = 125 viewsCalculate Total Views Next 7 Days: Calculate the total number of views for the next 7 days, starting from the 366th day, with a 25% daily increase. We will use the formula for the sum of a geometric series since the number of views is increasing by a constant percentage each day. The formula for the sum of the first n terms of a geometric series is S_n = a * (1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms. In this case, a = 125 views, r = 1.25 (since there's a 25% increase each day), and n = 7. S_7 = 125 * (1 - 1.25^7) / (1 - 1.25)Perform Geometric Series Calculation: Perform the calculation for the sum of the geometric series. S_7 = 125 * (1 - 1.25^7) / (1 - 1.25) S_7 = 125 * (1 - 17.37890625) / (-0.25) S_7 = 125 * (-16.37890625) / (-0.25) S_7 = -2047.36328125 / (-0.25) S_7 = 8189.453125Calculate More Views: Calculate how many more views the video received in the 7-day period after the first 365 days compared to the first 365 days. We subtract the total number of views for the first 365 days from the total number of views for the next 7 days. More views = 8189.453125 views - 36,500 views This calculation is incorrect because we should be adding the views from the first 365 days to the views from the next 7 days, not subtracting them. This is a math error.

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