Question

In Example 43.9 (Section 43.4), the activity of atmospheric carbon before $\mathbf{1900}$was given. Discuss why this activity may have changed since$\mathbf{1900}$.

Short answer

The activity has changed since $1900$ because of the increase in the carbon dioxide in the atmosphere over the regular rate$1900$ that results in the contamination caused by the industrial activities, mainly in the coal-powered factories.

Step-by-step solution

Define the activity.

The rate of change of $N\left(t\right)$is the negative quantity $\raisebox{1ex}{$dN\left(t\right)$}\!\left/ \!\raisebox{-1ex}{$dt$}\right.$thus $-\raisebox{1ex}{$dN\left(t\right)$}\!\left/ \!\raisebox{-1ex}{$dt$}\right.$is called the decay rate or the activity.

The activity is directly proportional to $N\left(t\right)$; it equals a constant $\lambda$multiply by $N\left(t\right)$:

$-\raisebox{1ex}{$dN\left(t\right)$}\!\left/ \!\raisebox{-1ex}{$dt$}\right.=\lambda N\left(t\right)$

Explanation.

The increase in the carbon dioxide in the atmosphere over the regular rate$1900$ due to those results in the contamination caused by the industrial activities, mainly in the coal-powered factories.

Hence, the activity has changed since $1900$.