Chapter 10, Problem 5EFA

To determine

The total annual growth in the carbon footprint in metric tons of carbon dioxide per year for each of the five countries in the table by assuming that a hectare $\left(1.0\text{ hectare }=0.01\text{ square kilometer}\right)$ of tropical rain forest absorbs 0.85 metric tons $\left(1\text{metric ton}\text{=}\text{2,200}\text{pounds}\right)$ of carbon dioxide per year.

Answer to Problem 5EFA

Country	Area of Tropical Rain Forest (square kilometers)	Area of Deforestation per Year (square kilometers)	Total carbon footprint per year for tropical rain forest (metric tons)
A	1,800,000	50,000	4,250,000
B	55,000	3,000	255,000
C	22,000	6,000	510,000
D	530,000	12,000	1,020,000
E	80,000	700	59,500

Explanation of Solution

Given info:

Country	Area of Tropical Rain Forest (square kilometers)	Area of Deforestation per Year (square kilometers)
A	1,800,000	50,000
B	55,000	3,000
C	22,000	6,000
D	530,000	12,000
E	80,000	700

The expression that can be used to calculate total annual growth in the carbon footprint in metric tons of carbon dioxide per year is as follows:

$\left\{\begin{array}{l}\text{Total annual growth in }\\ \text{the carbon footprint}\end{array}\right\}\text{=}\left(\text{Area of deforestation per year}\right)\times \left(\frac{1\text{hectare}}{0.01\text{sq}\text{.km}}\right)\times 0.85$

To determine the total annual growth in the carbon footprint in metric tons of carbon dioxide per year in Country A, substitute the value of area of deforestation as 50,000 sq.km. Then, the following result is obtained:

$\begin{array}{c}\left\{\begin{array}{l}\text{Total annual growth in}\text{the }\\ \text{carbon footprint}\text{in}\text{Country}\text{A}\end{array}\right\}\text{=}\left(50,000\right)\times \left(\frac{1\text{hectare}}{0.01\text{sq}\text{.km}}\right)\times 0.85\\ =4250000\text{metric}\text{tons}\text{per}\text{year}\end{array}$

Similarly, the following result is obtained:

$\begin{array}{c}\left\{\begin{array}{l}\text{Total annual growth in}\text{the }\\ \text{carbon footprint}\text{in}\text{Country}\text{B}\end{array}\right\}\text{=}\left(3,000\right)\times \left(\frac{1\text{hectare}}{0.01\text{sq}\text{.km}}\right)\times 0.85\\ =255,000\text{metric}\text{tons}\text{per}\text{year}\end{array}$

$\begin{array}{c}\left\{\begin{array}{l}\text{Total annual growth in}\text{the }\\ \text{carbon footprint}\text{in}\text{Country}\text{B}\end{array}\right\}\text{=}\left(6,000\right)\times \left(\frac{1\text{hectare}}{0.01\text{sq}\text{.km}}\right)\times 0.85\\ =510,000\text{metric}\text{tons}\text{per}\text{year}\end{array}$

$\begin{array}{c}\left\{\begin{array}{l}\text{Total annual growth in}\text{the }\\ \text{carbon footprint}\text{in}\text{Country}\text{B}\end{array}\right\}\text{=}\left(12,000\right)\times \left(\frac{1\text{hectare}}{0.01\text{sq}\text{.km}}\right)\times 0.85\\ =1,020,000\text{metric}\text{tons}\text{per}\text{year}\end{array}$

$\begin{array}{c}\left\{\begin{array}{l}\text{Total annual growth in}\text{the }\\ \text{carbon footprint}\text{in}\text{Country}\text{B}\end{array}\right\}\text{=}\left(700\right)\times \left(\frac{1\text{hectare}}{0.01\text{sq}\text{.km}}\right)\times 0.85\\ =59,500\text{metric}\text{tons}\text{per}\text{year}\end{array}$