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On the first day it was posted online, a music video got 1000 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 24 days, to the nearest whole number? Answer:

On the first day it was posted online, a music video got 10001000 views. The number of views that the video got each day increased by 20% 20 \% per day. How many total views did the video get over the course of the first 2424 days, to the nearest whole number?\newlineAnswer:

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Q. On the first day it was posted online, a music video got 10001000 views. The number of views that the video got each day increased by 20% 20 \% per day. How many total views did the video get over the course of the first 2424 days, to the nearest whole number?\newlineAnswer:
  1. Identify initial views and rate: Identify the initial number of views and the daily increase rate.\newlineThe initial number of views V0V_0 is 10001000, and the daily increase rate rr is 20%20\% or 0.200.20 in decimal form.
  2. Determine total views formula: Determine the formula for the total number of views after a certain number of days.\newlineThe total number of views VtotalV_{\text{total}} after nn days can be calculated using the formula for the sum of a geometric series: Vtotal=V0×[1−rn1−r]V_{\text{total}} = V_0 \times \left[\frac{1 - r^n}{1 - r}\right], where rr is the common ratio (1+daily increase rate)(1 + \text{daily increase rate}).
  3. Calculate common ratio: Calculate the common ratio for the geometric series.\newlineThe common ratio rr is 1+1 + the daily increase rate, which is 1+0.20=1.201 + 0.20 = 1.20.
  4. Calculate total views after 2424 days: Calculate the total number of views after 2424 days using the formula. Vtotal=1000×[(1−1.2024)(1−1.20)]V_{\text{total}} = 1000 \times \left[\frac{(1 - 1.20^{24})}{(1 - 1.20)}\right]
  5. Evaluate expression: Evaluate the expression.\newlineFirst, calculate 1.20241.20^{24}, then substitute it into the formula and solve for VtotalV_{\text{total}}.\newline1.2024=9.646293321.20^{24} = 9.64629332 (rounded to 88 decimal places)\newlineVtotal=1000×[(1−9.64629332)(1−1.20)]V_{\text{total}} = 1000 \times \left[\frac{(1 - 9.64629332)}{(1 - 1.20)}\right]
  6. Continue calculation: Continue the calculation.\newlineVtotal=1000×[−8.64629332−0.20]V_{\text{total}} = 1000 \times \left[\frac{-8.64629332}{-0.20}\right]
  7. Simplify expression: Simplify the expression. Vtotal=1000×43.2314666V_{\text{total}} = 1000 \times 43.2314666
  8. Calculate final value: Calculate the final value. Vtotal=43231.4666V_{\text{total}} = 43231.4666 Since we need to round to the nearest whole number, the total number of views is approximately 4323143231.

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