Global Warming The increase in carbon dioxide (CO2) in the atmosphere is a major cause of global

step 1 Now, we're told that the increasing carbon dioxide in atmosphere is a major cause of global warn

Global Warming The increase in carbon dioxide (CO2) in the...

Global Warming The increase in carbon dioxide $\left(\mathrm{CO}_{2}\right)$ in the atmosphere is a major cause of global warming. Using data obtained by Charles David Keeling, professor at Scripps Institution of Oceanography, the average amount of $\mathrm{CO}_{2}$ in the atmosphere from 1958 through 2013 is approximated by $$A(t)=0.012414 t^{2}+0.7485 t+313.9 \quad(1 \leq t \leq 58)$$ where $A(t)$ is measured in parts per million volume (ppmv) and $t$ in years, with $t=1$ corresponding to 1958. a. What can you say about the rate of change of the average amount of atmospheric $\mathrm{CO}_{2}$ from 1958 through $2013 ?$ b. What can you say about the rate of change of the rate of change of the average amount of atmospheric $\mathrm{CO}_{2}$ from 1958 through $2013 ?$

Global Warming The increase in carbon dioxide $\left(\mathrm{CO}_{2}\right)$ in the atmosphere is a major cause of global warming. Using data obtained by Charles David Keeling, professor at Scripps Institution of Oceanography, the average amount of $\mathrm{CO}_{2}$ in the atmosphere from 1958 through 2013 is approximated by
$$A(t)=0.012414 t^{2}+0.7485 t+313.9 \quad(1 \leq t \leq 58)$$
where $A(t)$ is measured in parts per million volume (ppmv) and $t$ in years, with $t=1$ corresponding to 1958.
a. What can you say about the rate of change of the average amount of atmospheric $\mathrm{CO}_{2}$ from 1958 through $2013 ?$
b. What can you say about the rate of change of the rate of change of the average amount of atmospheric $\mathrm{CO}_{2}$ from 1958 through $2013 ?$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Derivative

The derivative of a function represents the instantaneous rate of change of that function with respect to a variable. It is a fundamental concept in calculus used to determine how rapidly a quantity changes over time or another variable. In real-world applications, such as in environmental science, the derivative helps in understanding trends like the increase in atmospheric gas concentrations.

Second Derivative

The second derivative of a function measures the rate of change of the first derivative, providing insight into the acceleration or deceleration of the original function. It is useful in determining the concavity of a function, which tells us whether the rate of change is increasing or decreasing. This concept is essential for assessing whether variations in phenomena, such as the speed of temperature or CO2 increases, are themselves growing or slowing down.

Mathematical Modeling

Mathematical modeling involves using mathematical expressions, such as functions or equations, to represent and analyze real-world phenomena. By approximating complex systems with models, scientists and researchers can make predictions and gain insights into trends, such as changes in atmospheric conditions over time. Such models help bridge the gap between theoretical mathematics and practical applications like environmental studies.

Transcript

Please give Ace some feedback