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 for first 365 days: First, let's rephrase the  ＂How many more views did Eitan's video receive in the 7-day period after the first 365 days compared to the first 365 days?＂Calculate views on the 366th day: Calculate the total number of views for the first 365 days. 100 views/day * 365 days = 36,500 viewsCalculate sum of views for 7 days after the 365th day: Now, let's calculate the number of views on the 366th day. Since the views grew by 25% from the original 100 views per day, the views on the 366th day would be: 100 views + (25/100 * 100 views) = 125 viewsEvaluate the sum: For the subsequent days, the number of views will increase by 25% each day. This is a geometric sequence where the first term is 125 views and the common ratio is 1.25 (since 25% increase is the same as multiplying by 1.25). We need to find the sum of views for 7 days starting from the 366th day. The sum of a geometric series is given by 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, r = 1.25, and n = 7.Calculate more views in the 7-day period after the first 365 days: Calculate the sum of the geometric series for the 7 days after the 365th day. S_7 = 125 * (1 - 1.25^7) / (1 - 1.25)Evaluate the sum S_7. 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 are looking for an integer number of views, we can round this to 8,189 views.Now, we need to find out how many more views the video received in the 7-day period after the first 365 days compared to the first 365 days. More views = S_7 - 36,500 More views = 8,189 - 36,500 This calculation is incorrect because we should be adding the views from the 7-day period to the initial 36,500 views, not subtracting. This is a math error.

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