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A controversial story comes out in the school newspaper. The number of students who have not heard about the story decreases at a rate that is proportional at any time to the number of students who have not heard the story at that time. There were 900 students who had not heard the story initially, and the number of students is divided by 3 every 4 days. How many students have not heard the story after 7 days? Round to the nearest student. students

A controversial story comes out in the school newspaper. The number of students who have not heard about the story decreases at a rate that is proportional at any time to the number of students who have not heard the story at that time.\newlineThere were 900900 students who had not heard the story initially, and the number of students is divided by 33 every 44 days.\newlineHow many students have not heard the story after 77 days?\newlineRound to the nearest student.\newline□\square students

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Q. A controversial story comes out in the school newspaper. The number of students who have not heard about the story decreases at a rate that is proportional at any time to the number of students who have not heard the story at that time.\newlineThere were 900900 students who had not heard the story initially, and the number of students is divided by 33 every 44 days.\newlineHow many students have not heard the story after 77 days?\newlineRound to the nearest student.\newline□\square students
  1. Understand and Determine Decay Type: Understand the problem and determine the type of decay. The problem states that the number of students who have not heard the story decreases at a rate proportional to the number of students who have not heard it at any given time. This is an example of exponential decay.
  2. Identify Initial Quantity and Rate: Identify the initial quantity and the decay rate.\newlineThe initial number of students who have not heard the story is 900900. The number of students is divided by 33 every 44 days, which means after 44 days, only one-third of the students have not heard the story.
  3. Calculate Decay Factor: Calculate the decay factor for each 44-day period.\newlineThe decay factor for each 44-day period is 13\frac{1}{3}, as the number of students who have not heard the story is divided by 33.
  4. Determine Complete Periods: Determine the number of complete 44-day periods in 77 days.\newlineSince 77 days is not a multiple of 44, we have one complete 44-day period and an additional 33 days. We will first calculate the number of students who have not heard the story after the complete 44-day period.
  5. Calculate Students After 44 Days: Calculate the number of students who have not heard the story after the complete 44-day period.\newlineNumber of students after 44 days == Initial number of students // Decay factor\newline=900/3= 900 / 3\newline=300= 300 students
  6. Determine Daily Decay Rate: Determine the daily decay rate.\newlineSince the number of students is divided by 33 every 44 days, we need to find the equivalent daily decay rate. The daily decay rate is the fourth root of 13\frac{1}{3} because (13)14(\frac{1}{3})^{\frac{1}{4}} raised to the power of 44 equals 13\frac{1}{3}.
  7. Calculate Fourth Root: Calculate the fourth root of 13\frac{1}{3} to find the daily decay rate.\newlineDaily decay rate = (13)14(\frac{1}{3})^{\frac{1}{4}}
  8. Calculate Students After 33 Days: Calculate the number of students who have not heard the story after the additional 33 days.\newlineNumber of students after 77 days = Number of students after 44 days ×\times (Daily decay rate)3^3
  9. Perform Calculation: Perform the calculation for the number of students after 77 days.\newlineNumber of students after 77 days = 300×(13)34300 \times (\frac{1}{3})^{\frac{3}{4}}
  10. Calculate Exact Value: Calculate the exact value and round to the nearest student.\newlineNumber of students after 77 days ≈300×(13)34\approx 300 \times (\frac{1}{3})^{\frac{3}{4}}

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