Problem

A small country emits 70,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by $2 \%$ per year for the next 14 years. In the first year of the agreement, the country will keep its emissions at 70,000 kilotons and the emissions will decrease $2 \%$ 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 niumber?

Solution

Step 1 :This problem can be solved using the formula for the sum of a geometric series, which is \(S = a \frac{1 - r^n}{1 - r}\), where \(a\) is the first term, \(r\) is the common ratio, and \(n\) is the number of terms.

Step 2 :In this case, the first term \(a\) is the initial amount of carbon dioxide emissions, which is 70,000 kilotons.

Step 3 :The common ratio \(r\) is 0.98, because the emissions decrease by 2% each year.

Step 4 :The number of terms \(n\) is 14, because the agreement lasts for 14 years.

Step 5 :Substituting these values into the formula, we get \(S = 70000 \frac{1 - (0.98)^{14}}{1 - 0.98}\).

Step 6 :Solving this equation gives us the total amount of carbon dioxide emissions over the 14 year period.

Step 7 :The final answer is approximately \(\boxed{862253}\) kilotons of carbon dioxide.

From Solvely APP
Source: https://solvelyapp.com/problems/39139/

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