A small country emits 54,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 4% per year for the next 14 years. In the first year of the agreement, the country will keep its emissions at 54,000 kilotons and the emissions will decrease 4% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 14 year period, to the nearest whole number? Answer:

Question

A small country emits 54,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by  4% per year for the next 14 years. In the first year of the agreement, the country will keep its emissions at 54,000 kilotons and the emissions will decrease  4% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 14 year period, to the nearest whole number? Answer:

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. We need to calculate the total carbon emissions over 14 years, with a 4% reduction each year after the first year. The initial emission is 54,000 kilotons.Calculate emissions for each year: Calculate the emissions for each year. The emissions for the first year are 54,000 kilotons. For each subsequent year, the emissions are 4% less than the previous year.Use sum formula for series: Use the formula for the sum of a decreasing geometric series. The sum S of n terms of a geometric series with first term a and common ratio r is given by S = a(1 - r^n) / (1 - r), where 0 < r < 1. In this case, a = 54,000 kilotons, r = 0.96 (since there's a 4% reduction, 100% - 4% = 96% = 0.96), and n = 14.Calculate total emissions: Calculate the total emissions. S = 54,000 * (1 - 0.96^14) / (1 - 0.96) First, calculate 0.96^14.Calculate 0.96^14: Calculate 0.96^14. 0.96^14 ≈ 0.563Substitute into sum formula: Substitute 0.96^14 into the sum formula. S = 54,000 * (1 - 0.563) / (1 - 0.96)Calculate numerator of sum: Calculate the numerator of the sum formula. 1 - 0.563 = 0.437 S = 54,000 * 0.437 / (1 - 0.96)Calculate denominator of sum: Calculate the denominator of the sum formula. 1 - 0.96 = 0.04 S = 54,000 * 0.437 / 0.04Calculate total emissions: Calculate the total emissions S. S = 54,000 * 0.437 / 0.04 S = 54,000 * 10.925 S ≈ 590,550 kilotonsRound total emissions: Round the total emissions to the nearest whole number. S ≈ 590,550 kilotons

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