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

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Calculate Total Views: Calculate the total number of views for the first 365 days. Since the video received approximately 100 views per day, we multiply the number of days by the number of views per day. 365 days * 100 views/day = 36,500 viewsDetermine 366th Day Views: Determine the number of views on the 366th day. Since the views grew at a rate of 25% per day starting on the 366th day, we calculate the views for that day. 100 views * (1 + 0.25) = 125 viewsCalculate Total Views Next 7 Days: Calculate the total number of views for the next 7 days, including the 25% growth rate per day. We use the formula for the sum of a geometric series: 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. Here, a = 125 views, r = 1.25 (since the growth rate is 25%), 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 = 125 * 65.515625 S_7 = 8,189.453125 Since we cannot have a fraction of a view, we round to the nearest whole number. S_7 ≈ 8,189 viewsCompare Total Views: Compare the total number of views in the 7-day period after the first 365 days to the number of views in the first 365 days. We subtract the number of views in the first 365 days from the number of views in the 7-day period. 8,189 views - 36,500 views This calculation does not make sense because we are asked to find how many more views were received in the 7-day period after the first 365 days, not the difference between the two periods. We need to compare the additional views received in the 7-day period to the original 36,500 views.

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