Question

A small country emits 92,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 5% per year for the next 15 years. In the first year of the agreement, the country will keep its emissions at 92,000 kilotons and the emissions will decrease 5% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 15 year period, to the nearest whole number?

Answer 1

To calculate the total amount of carbon dioxide emitted over the course of 15 years, we can start with the initial amount of 92,000 kilotons and multiply by 0.95 (the reduction factor) each year.

Explanation:

Year 1: 92,000 kilotons

Year 2: 92,000 * 0.95 = 87,400 kilotons

Year 3: 87,400 * 0.95 = 82,990 kilotons

and so on, until year 15.

To find the total amount of carbon dioxide emitted over the course of 15 years, we need to sum up the emissions for each year:

92,000 + 87,400 + 82,990 + ... + (92,000 * 0.95^14) = 92,000 * (1 + 0.95 + 0.95^2 + ... + 0.95^14)

This is a finite geometric series and can be calculated using the formula for the sum of a finite geometric series:

S = a * (1 - r^n) / (1 - r),

where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.

For this series, a = 92,000, r = 0.95, and n = 15. Plugging these values into the formula, we get:

S = 92,000 * (1 - 0.95^15) / (1 - 0.95)

S = 92,000 * (1 - 0.556774) / 0.05

S = 92,000 * 0.443226 / 0.05

S = 92,000 * 8.86452

S = 814,178.24 kilotons

Rounding to the nearest whole number, the country would emit 814,178 kilotons of carbon dioxide over the course of 15 years.