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A major fishing company does its fishing in a local lake. The first year of the company's operations it managed to catch 170,000 fish. Due to population decreases, the number of fish the company was able to catch decreased by 6% each year. How many total fish did the company catch over the first 11 years, to the nearest whole number? Answer:

A major fishing company does its fishing in a local lake. The first year of the company's operations it managed to catch 170170,000000 fish. Due to population decreases, the number of fish the company was able to catch decreased by 6% 6 \% each year. How many total fish did the company catch over the first 1111 years, to the nearest whole number?\newlineAnswer:

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Q. A major fishing company does its fishing in a local lake. The first year of the company's operations it managed to catch 170170,000000 fish. Due to population decreases, the number of fish the company was able to catch decreased by 6% 6 \% each year. How many total fish did the company catch over the first 1111 years, to the nearest whole number?\newlineAnswer:
  1. Understand the problem: Understand the problem.\newlineThe company starts with catching 170,000170,000 fish in the first year. Each subsequent year, the catch decreases by 6%6\%. We need to calculate the total number of fish caught over 1111 years.
  2. Determine initial catch: Determine the initial number of fish caught.\newlineThe initial number of fish caught in the first year is 170,000170,000.
  3. Calculate yearly catch: Calculate the number of fish caught each year.\newlineThe number of fish caught each year follows a geometric sequence where each term is 94%94\% (100%−6%100\% - 6\%) of the previous term.
  4. Use geometric series formula: Use the formula for the sum of a geometric series.\newlineThe sum of a geometric series is given by Sn=a(1−rn)/(1−r)S_n = a(1 - r^n) / (1 - r), where aa is the first term, rr is the common ratio, and nn is the number of terms.
  5. Substitute values into formula: Substitute the values into the formula.\newlineHere, a=170,000a = 170,000, r=0.94r = 0.94 (since the catch decreases by 6%6\%, the remaining percentage is 94%94\%), and n=11n = 11.\newlineS11=170,000(1−0.9411)/(1−0.94)S_{11} = 170,000(1 - 0.94^{11}) / (1 - 0.94)
  6. Calculate the sum: Calculate the sum.\newlineS11=170,000(1−0.9411)/(1−0.94)S_{11} = 170,000(1 - 0.94^{11}) / (1 - 0.94)\newlineS11=170,000(1−0.558405)/0.06S_{11} = 170,000(1 - 0.558405) / 0.06\newlineS11=170,000(0.441595)/0.06S_{11} = 170,000(0.441595) / 0.06\newlineS11=170,000×7.35992S_{11} = 170,000 \times 7.35992\newlineS11=1,251,188.4S_{11} = 1,251,188.4
  7. Round to nearest whole number: Round to the nearest whole number.\newlineThe total number of fish caught over the first 1111 years, rounded to the nearest whole number, is 1,251,1881,251,188.

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