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First-Order Decay Concentration

Mediumkineticsdecay
A conservative substance decays by first-order kinetics with rate constant k = 0.35 per day. Starting at 100 mg/L, the concentration remaining after 4 days is most nearly:
  1. A14 mg/L
  2. B25 mg/L
  3. C40 mg/L
  4. D65 mg/L
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Answer: B. 25 mg/L

First-order decay gives C = C₀e^(−kt) = 100e^(−(0.35)(4)) = 100e^(−1.40) ≈ 25 mg/L. Treating the decay as linear, 100(1 − 0.35 × 4), would give zero and shows why the exponential form matters once kt approaches one.
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