Q: In 1960, the atmospheric concentration of carbon dioxide was measured at 317 ppm. By 2010, it had risen to 389 ppm. What was the total increase in carbon dioxide concentration over this period?

$$389\ \text{ppm} - 317\ \text{ppm} = 72\ \text{ppm}$$

Q: What is the average rate of increase in atmospheric carbon dioxide concentration between 1960 and 2010?

$$\frac{72\ \text{ppm}}{50\ \text{years}} = 1.44\ \text{ppm/year}$$

Q: If the average rate of increase in carbon dioxide concentration from 1960 to 2010 continues, what would be the estimated concentration in 2050?

$$389\ \text{ppm} + (1.44\ \text{ppm/year} \times 40\ \text{years}) = 446.6\ \text{ppm}$$

Q: A scientist wants to calculate the average rate of change in atmospheric CO$$_2$$ between 1880 (290 ppm) and 1920 (303 ppm). What is the correct calculation?

$$\frac{303\ \text{ppm} - 290\ \text{ppm}}{1920 - 1880} = \frac{13\ \text{ppm}}{40\ \text{years}} = 0.325\ \text{ppm/year}$$

Q: Suppose the concentration of atmospheric CO$$_2 in 2020 is 415 $$ppm. If the rate of increase from 2010 to 2020 is the same as from 1960 to 2010, what is the expected concentration in 2030?

$$415\ \text{ppm} + (1.44\ \text{ppm/year} \times 10\ \text{years}) = 429.4\ \text{ppm}$$

Q: If the concentration of CO$$_2$$ increased by 56 ppm from 2010 to 2050, what was the average annual rate of increase during this period?

$$\frac{56\ \text{ppm}}{40\ \text{years}} = 1.4\ \text{ppm/year}$$

Q: Which of the following is the correct formula to estimate a future concentration, given a starting concentration, a constant rate of increase, and a number of years?

$$\text{Future concentration} = \text{Starting concentration} + (\text{Rate} \times \text{Number of years})$$

Question 1

In 1960, the atmospheric concentration of carbon dioxide was measured at 317 ppm. By 2010, it had risen to 389 ppm. What was the total increase in carbon dioxide concentration over this period?

Accepted Answer

$$389\ 	ext{ppm} - 317\ 	ext{ppm} = 72\ 	ext{ppm}$$

Question 2

What is the average rate of increase in atmospheric carbon dioxide concentration between 1960 and 2010?

Accepted Answer

$$\frac{72\ 	ext{ppm}}{50\ 	ext{years}} = 1.44\ 	ext{ppm/year}$$

Question 3

If the average rate of increase in carbon dioxide concentration from 1960 to 2010 continues, what would be the estimated concentration in 2050?

Accepted Answer

$$389\ 	ext{ppm} + (1.44\ 	ext{ppm/year} 	imes 40\ 	ext{years}) = 446.6\ 	ext{ppm}$$

Question 4

Which of the following best explains why the average rate of increase in atmospheric carbon dioxide might be different between 1880–1920 and 1960–2010?

Accepted Answer

Industrialization and increased fossil fuel use after 1960 accelerated the rate of carbon dioxide emissions.

Question 5

A scientist wants to calculate the average rate of change in atmospheric CO$$_2$$ between 1880 (290 ppm) and 1920 (303 ppm). What is the correct calculation?

Accepted Answer

$$\frac{303\ 	ext{ppm} - 290\ 	ext{ppm}}{1920 - 1880} = \frac{13\ 	ext{ppm}}{40\ 	ext{years}} = 0.325\ 	ext{ppm/year}$$

Question 6

Why is it important to use the difference between the final and initial values when calculating the change in a quantity over time?

Accepted Answer

It accurately reflects the net change, avoiding confusion with total or average values.

Question 7

Suppose the concentration of atmospheric CO$$_2 in 2020 is 415 $$ppm. If the rate of increase from 2010 to 2020 is the same as from 1960 to 2010, what is the expected concentration in 2030?

Accepted Answer

$$415\ 	ext{ppm} + (1.44\ 	ext{ppm/year} 	imes 10\ 	ext{years}) = 429.4\ 	ext{ppm}$$

Question 8

A student claims that the rate of increase in CO$$_2$$ concentration is always constant. Which of the following best evaluates this claim?

Accepted Answer

The rate can change due to factors such as industrialization, policy changes, and natural events.

Question 9

If the concentration of CO$$_2$$ increased by 56 ppm from 2010 to 2050, what was the average annual rate of increase during this period?

Accepted Answer

$$\frac{56\ 	ext{ppm}}{40\ 	ext{years}} = 1.4\ 	ext{ppm/year}$$

Question 10

Which of the following is the correct formula to estimate a future concentration, given a starting concentration, a constant rate of increase, and a number of years?

Accepted Answer

$$	ext{Future concentration} = 	ext{Starting concentration} + (	ext{Rate} 	imes 	ext{Number of years})$$

Question 11

A graph shows a steady increase in atmospheric CO$$_2$$ over time. Which of the following best describes the relationship between time and CO$$_2$$ concentration?

Accepted Answer

A positive linear relationship, where CO$$_2$$ concentration increases as time increases.

Question 12

If a new technology reduces the rate of CO$$_2$$ increase by half after 2020, what would be the estimated concentration in 2050, starting from 415 ppm in 2020 and using the previous rate of $$1.44\ 	ext{ppm/year}$$?

Accepted Answer

$$415\ 	ext{ppm} + (0.72\ 	ext{ppm/year} 	imes 30\ 	ext{years}) = 436.6\ 	ext{ppm}$$

Question 13

Which of the following real-world events could most likely cause a significant change in the rate of atmospheric CO$$_2$$ increase?

Accepted Answer

A global shift from fossil fuels to renewable energy sources.

Interpreting Graphs: Atmospheric Carbon Dioxide Levels

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