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 number?

This problem describes a situation where a country's carbon dioxide emissions decrease by 2% per year over a 14-year period. We need to calculate the total emissions during these 14 years.

### Step-by-step approach:

1. **Initial emissions**: In the first year, the emissions are 70,000 kilotons.
2. **Subsequent years**: Each year, the emissions are reduced by 2%. Therefore, in the second year, the emissions will be \( 70,000 \times (1 - 0.02) = 70,000 \times 0.98 \), and in the third year, they will be \( 70,000 \times 0.98^2 \), and so on.

Thus, the emissions in the \( n \)-th year can be expressed as:
\[
E_n = 70,000 \times 0.98^{n-1}
\]
where \( E_n \) is the emissions in year \( n \).

3. **Total emissions over 14 years**: The total emissions over the 14-year period will be the sum of the emissions for each year. Mathematically, this can be represented as:
\[
\text{Total Emissions} = E_1 + E_2 + \cdots + E_{14}
\]
This forms a geometric series with:
- First term \( a = 70,000 \)
- Common ratio \( r = 0.98 \)
- Number of terms \( n = 14 \)

The sum \( S \) of a geometric series is given by:
\[
S = a \times \frac{1 - r^n}{1 - r}
\]
Substituting the values:
\[
S = 70,000 \times \frac{1 - 0.98^{14}}{1 - 0.98}
\]

Now, let's calculate this value.

The total carbon dioxide emissions over the 14-year period, with a 2% reduction per year, would be approximately 862,253 kilotons.

Would you like more details or have any questions?

Here are some related questions:
1. How would the total emissions change if the reduction was 3% instead of 2%?
2. What if the emissions increased by 1% per year instead of decreasing?
3. How can the country achieve net-zero emissions over the next 50 years with similar reduction percentages?
4. How do cumulative emissions impact global warming and climate change?
5. What is the mathematical formula for predicting emissions beyond 14 years?

**Tip**: When dealing with percentage changes over time, geometric series are a useful tool for calculating totals.

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 number?

Find out how a country's carbon dioxide emissions, starting at 70,000 kilotons and decreasing by 2% annually, result in a total emission of 862,253 kilotons over 14 years. This problem involves geometric series and exponential decay, suitable for high school math students.

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