The concentration of pollutants in a stream is given by $y=.06 e^{-3 x}$, where $y$ is the amount of pollutant in grams per liter and $x$ is the distance, in kilometers, downstream from the source of the pollution. Match each question with one of the solutions A, B, C, or D.
-How far downstream is the pollutant level half the amount at the source?
A) Solve $.02=.06 e^{-3 x}$
B) Solve $\frac{1}{2}(.06)=.06 e^{-3 x}$
C) Evaluate $.06 e^{-3(.02)}$
D) Evaluate $.06 e^{-3(1 / 2)}$

Question

Quizplus · Accepted Answer

To find the distance downstream where the pollutant level is half of its initial amount, we need to solve for $x$ when $y$ is half of its initial value, which is $.06$. Halving the initial concentration gives $\frac{1}{2}(.06) = .03$, leading to the equation $.03 = .06 e^{-3x}$, which matches option B.

The Concentration of Pollutants in a Stream Is Given By y=.06