Downstream from a waste treatment plant the amount of dissolved oxygen in the wa

Question

Downstream from a waste treatment plant the amount of dissolved oxygen in the water usually decreases for some distance (due to bacteria consuming the oxygen) and then increases (due to natural purification). . The amount of dissolved oxygen is usually taken as a measure of of the health of the river. Suppose that the amount of dissolved oxygen x miles down stream is D(x) = 0.2x^2 - 2x +10 mpt (milligrams per liter) for x greater than or equal to 0 and less than or equal to 20. Use this formula to find the instantaneous rate of change of the dissolved oxygen: a.) 1 mile downstream b.) 10 miles downstream interpret the sign of your answers

Explanation / Answer

instantaneous rate of change = D'(x) = 0.2*2x - 2 + 0 = 0.4x - 2

a)

D'(1) = 0.4 - 2 = -1.6 -> negative rate -> dissolved oxygen is decreasing.

b)

D'(1) = 0.4*10 - 2 = 2 -> positive rate -> dissolved oxygen is increasing.

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.