Questions: The bar graph gives the average atmospheric concentration of carbon dioxide. a. Estimate the yearly increase in the average atmospheric concentration of carbon dioxide. Express the answer in parts per million. b. Write a mathematical model that estimates the average atmospheric concentration of carbon dioxide, C, in parts per million, x years after 1950. c. If the trend shown by the data continues, use your mathematical model from part (b) to project the average atmospheric concentration of carbon dioxide in 2025.

Solution Steps

To estimate the yearly increase, we need to find the difference in the average atmospheric concentration of carbon dioxide between two years and divide by the number of years between them.

From the graph:

• In 1950, the concentration is 311 ppm.
• In 2015, the concentration is 405 ppm.

The difference in concentration is: \[ 405 \, \text{ppm} - 311 \, \text{ppm} = 94 \, \text{ppm} \]

The number of years between 1950 and 2015 is: \[ 2015 - 1950 = 65 \, \text{years} \]

The yearly increase is: \[ \frac{94 \, \text{ppm}}{65 \, \text{years}} \approx 1.4 \, \text{ppm/year} \]

Using the yearly increase calculated in Step 1, we can write a linear model. Let \( C \) be the concentration in ppm and \( x \) be the number of years after 1950.

The model is: \[ C = 311 + 1.4x \]

To project the concentration in 2025, we need to find \( x \) for the year 2025: \[ x = 2025 - 1950 = 75 \]

Using the model \( C = 311 + 1.4x \): \[ C = 311 + 1.4 \times 75 \] \[ C = 311 + 105 \] \[ C = 416 \, \text{ppm} \]

Final Answer