Dose Response Curve

Pesticide Y kills 50% of the fish at 40 mg/kg, so its LD50 is 40 mg/kg.

• Answer: 40 mg/kg

Pesticide X kills 0% at 0, 10 and 20 mg/kg and 2% at 30 mg/kg, so its threshold lies at 20 mg/kg (between 20 and 30).

• Answer: 20 mg/kg

Compare LD50s by division: $\frac{80\,\text{mg/kg}}{40\,\text{mg/kg}}$$= 2$, so Y is twice as toxic.

• X is twice as toxic as Y, since its LD50 is twice as large: A larger LD50 means more pesticide is needed to kill, so X is less toxic.
• They are equally toxic, since both kill about 98% or more of the fish at 160 mg/kg: Toxicity is compared at the 50% point, where Y needs half the dose X does.
• Correct: Y is twice as toxic as X: its LD50 is half of X’s: Right: the LD50 of Y is 40 mg/kg and of X is 80 mg/kg, and $\frac{80}{40} = 2$.
• X is more toxic, since its curve keeps rising to a higher dose: X rises later because it is less toxic; more of it is needed for the same effect.

$80\,\frac{\text{mg}}{\text{kg}} \times 0.60\,\text{kg}$$= 48\,\text{mg}$ for each fish.

• Setup: $\frac{80\,\text{mg}}{\text{kg}} \cdot 0.6\,\text{kg}$; answer 48 mg

At every dose from 20 to 80 mg/kg, Y kills a larger percent of fish than X, and its threshold and LD50 are both lower.

• Correct: X, because a larger dose of it is needed before fish start to die: Right: X has the higher threshold (about 20 mg/kg) and the higher LD50 (80 mg/kg).
• Y, because its curve reaches 100% faster, so it breaks down sooner: How fast a curve rises with dose says nothing about how fast the pesticide breaks down.
• Y, because it kills fish at lower doses, so less of it reaches the pond: Killing fish at lower doses makes Y more dangerous to them, not less.
• Either one, because both kill about 98% or more of the fish at high doses: At the doses most likely in runoff, the low end of the curves, Y kills far more fish.