A small country emits $114$ , $000$ kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by $0.5 \%$ per year for the next $5$ years. In the first year of the agreement, the country will keep its emissions at $114$ , $000$ kilotons and the emissions will decrease $0.5 \%$ in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the $5$ year period, to the nearest whole number? $\newline$ Answer:

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Q. A small country emits

114

000

kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by

0.5 \%

per year for the next

5

years. In the first year of the agreement, the country will keep its emissions at

114

000

kilotons and the emissions will decrease

0.5 \%

in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the

5

year period, to the nearest whole number?

\newline

Answer:

Set up formula: Understand the problem and set up the formula for the first year. $\newline$ In the first year, the country will emit the same amount of carbon dioxide as it does currently, which is $114,000$ kilotons.
Calculate second year: Calculate the emissions for the second year. $\newline$ To find the emissions for the second year, we need to decrease the first year's emissions by $0.5\%$ . This is calculated as follows: $\newline$ Emissions for second year = Emissions for first year - ( $0.5\%$ of Emissions for first year) $\newline$ Emissions for second year = $114,000$ kilotons - ( $0.5/100 \times 114,000$ kilotons) $\newline$ Emissions for second year = $114,000$ kilotons - $570$ kilotons $\newline$ Emissions for second year = $113,430$ kilotons
Calculate third year: Calculate the emissions for the third year. $\newline$ We apply the same $0.5\%$ reduction to the emissions of the second year: $\newline$ Emissions for third year = Emissions for second year - ( $0.5\%$ of Emissions for second year) $\newline$ Emissions for third year = $113,430$ kilotons - ( $0.5/100 \times 113,430$ kilotons) $\newline$ Emissions for third year = $113,430$ kilotons - $567.15$ kilotons $\newline$ Emissions for third year $\approx 112,862.85$ kilotons
Calculate fourth year: Calculate the emissions for the fourth year. $\newline$ Again, we apply the $0.5\%$ reduction to the emissions of the third year: $\newline$ Emissions for fourth year = Emissions for third year - ( $0.5\%$ of Emissions for third year) $\newline$ Emissions for fourth year = $112,862.85$ kilotons - ( $0.5/100 \times 112,862.85$ kilotons) $\newline$ Emissions for fourth year $\approx 112,862.85$ kilotons - $564.31425$ kilotons $\newline$ Emissions for fourth year $\approx 112,298.54$ kilotons
Calculate fifth year: Calculate the emissions for the fifth year. $\newline$ We apply the $0.5\%$ reduction to the emissions of the fourth year: $\newline$ Emissions for fifth year = Emissions for fourth year - ( $0.5\%$ of Emissions for fourth year) $\newline$ Emissions for fifth year = $112,298.54$ kilotons - ( $0.5/100 \times 112,298.54$ kilotons) $\newline$ Emissions for fifth year $\approx 112,298.54$ kilotons - $561.4927$ kilotons $\newline$ Emissions for fifth year $\approx 111,737.05$ kilotons
Calculate total emissions: Add up the emissions for all five years to get the total emissions. $\newline$ Total emissions $= \text{Emissions for first year} + \text{Emissions for second year} + \text{Emissions for third year} + \text{Emissions for fourth year} + \text{Emissions for fifth year}$ $\newline$ Total emissions $\approx 114,000 + 113,430 + 112,862.85 + 112,298.54 + 111,737.05$ kilotons $\newline$ Total emissions $\approx 564,328.44$ kilotons
Round total emissions: Round the total emissions to the nearest whole number. $\newline$ Total emissions $\approx 564,328$ kilotons