Chapter 8, Problem 15P

In environmental engineering (a specialty area in civil engineering), the following equation can be used to compute the oxygen level c $\left(\text{mg}/\text{L}\right)$ in a river downstream from a sewage discharge:

$c=10-20\left(e^{-0.2x}-e^{-0.75x}\right)$

wherex is the distance downstream in kilometers.

(a) Determine the distance downstream where the oxygen level first falls to a reading of 5 mg/L. (Hint: It is within 2 km of the discharge.) Determine your answer to a 1% error. Note that levels of oxygen below 5 mg/L are generally harmful to game-fish such as trout and salmon.

(b) Determine the distance downstream at which the oxygen is at a minimum. What is the concentration at that location?