Olson Romero

01/04/2023 · Middle School

A coal-burning plant emits sulfur dioxide into the surrounding air. The concentration \( C(x) \), in parts per million, is given by the function \[ C(x)=\frac{0.9}{x^{2}} \] where \( x \) is the distance away from the plant in miles. Question \#1(a): Determine \( C^{\prime}(x) \) Question \#1(b): Recall that the derivative \( C^{\prime}(x) \), when evaluated at \( x=x_{1} \), yields the instantaneous rate of change of \( C(x) \) at \( x=x_{1} \). Determine the instantaneous rate of change of the sulfur dioxide concentration 5 miles from the plant.