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On the first day it was posted online, a music video got 2000 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 30 days, to the nearest whole number? Answer:

On the first day it was posted online, a music video got 20002000 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 3030 days, to the nearest whole number?\newlineAnswer:

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Q. On the first day it was posted online, a music video got 20002000 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 3030 days, to the nearest whole number?\newlineAnswer:
  1. Identify initial number of views: Identify the initial number of views and the daily increase rate.\newlineThe initial number of views V0V_0 is 20002000, and the daily increase rate rr is 20%20\% or 0.200.20 in decimal form.
  2. Determine formula for total views: Determine the formula for the total number of views after a certain number of days.\newlineThe total number of views VV after nn days can be calculated using the formula for the sum of a geometric series: V=V0×[1−rn1−r]V = 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 3030 days: Calculate the total number of views after 3030 days using the formula.\newlineSubstitute the values into the formula: V=2000×[(1−1.2030)(1−1.20)]V = 2000 \times \left[\frac{(1 - 1.20^{30})}{(1 - 1.20)}\right].
  5. Evaluate expression within brackets: Evaluate the expression within the brackets first.\newlineCalculate 1.20301.20^{30} and then subtract it from 11.
  6. Calculate denominator of fraction: Calculate the denominator of the fraction.\newlineThe denominator is 1−1.201 - 1.20, which is −0.20-0.20.
  7. Divide result by denominator: Divide the result from Step 55 by the result from Step 66. This will give us the total multiplier to be applied to the initial number of views.
  8. Multiply initial views by total multiplier: Multiply the initial number of views by the total multiplier to find the total number of views. This will give us the total number of views the video got over the course of the first 3030 days.
  9. Round result to nearest whole number: Round the result to the nearest whole number as the final answer.
  10. Perform calculations: Perform the calculations.\newlineFirst, calculate 1.20301.20^{30}: \newline1.2030≈237.376311.20^{30} \approx 237.37631\newlineThen, subtract this from 11: \newline1−237.37631≈−236.376311 - 237.37631 \approx -236.37631\newlineNow, divide by −0.20-0.20: \newline−236.37631/−0.20≈1181.88155-236.37631 / -0.20 \approx 1181.88155\newlineFinally, multiply by the initial number of views: \newline1181.88155×2000≈2363763.11181.88155 \times 2000 \approx 2363763.1\newlineRound to the nearest whole number: \newline2363763.1≈23637632363763.1 \approx 2363763

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