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A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got 184 responses, but the responses were declining by 25% each day. Assuming the pattern continued, how many total responses would the company get over the course of the first 9 days after the magazine was published, to the nearest whole number? Answer:

A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got 184184 responses, but the responses were declining by 25% 25 \% each day. Assuming the pattern continued, how many total responses would the company get over the course of the first 99 days after the magazine was published, to the nearest whole number?\newlineAnswer:

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Q. A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got 184184 responses, but the responses were declining by 25% 25 \% each day. Assuming the pattern continued, how many total responses would the company get over the course of the first 99 days after the magazine was published, to the nearest whole number?\newlineAnswer:
  1. Initial Data: Determine the initial number of responses and the daily decline rate.\newlineInitial responses on the first day: 184184\newlineDaily decline rate: 25%25\%
  2. Calculate Daily Responses: Calculate the number of responses for each subsequent day using the decline rate.\newlineDay 11: 184184 responses\newlineTo find the number of responses for the next day, we multiply the previous day's responses by the decline rate (as a decimal).\newlineDay 22: 184×(1−0.25)=184×0.75=138184 \times (1 - 0.25) = 184 \times 0.75 = 138 responses
  3. Continue Pattern: Continue the pattern for the remaining days.\newlineDay 33: 138×0.75=103.5138 \times 0.75 = 103.5 responses, rounded to the nearest whole number is 104104 responses.\newlineDay 44: 104×0.75=78104 \times 0.75 = 78 responses\newlineDay 55: 78×0.75=58.578 \times 0.75 = 58.5 responses, rounded to the nearest whole number is 5959 responses.\newlineDay 66: 59×0.75=44.2559 \times 0.75 = 44.25 responses, rounded to the nearest whole number is 4444 responses.\newlineDay 77: 44×0.75=3344 \times 0.75 = 33 responses\newlineDay 88: 33×0.75=24.7533 \times 0.75 = 24.75 responses, rounded to the nearest whole number is 2525 responses.\newlineDay 99: 10410400 responses, rounded to the nearest whole number is 10410411 responses.
  4. Total Responses: Add up the total number of responses from all 99 days.\newlineTotal responses = Day 11 + Day 22 + Day 33 + Day 44 + Day 55 + Day 66 + Day 77 + Day 88 + Day 99\newlineTotal responses = 184+138+104+78+59+44+33+25+19184 + 138 + 104 + 78 + 59 + 44 + 33 + 25 + 19\newlineTotal responses = 684684 responses

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