A drug is known to be ineffective after it has decomposed 30%. The original concentration of a sample was 500 units/ml. When analysed 20 months later, the concentration was found to be 420 units/ml. A

Question

A drug is known to be ineffective after it has decomposed 30%. The original concentration of a sample was 500 units/ml. When analysed 20 months later, the concentration was found to be 420 units/ml. Assuming that the decomposition is first order, what will be the expiration time (in month) of the drug? (ln 2 = 0.7, ln 5 = 1.6, ln 7 = 1.9)

Prashant Kotian · Accepted Answer

Correct answer: 0040. k = (1/20) ln(500/420) = (1/20) ln(25/21). Expiration occurs when 30% decomposes, so 70% remains (350 units). t_exp = (1/k) ln(500/350) = (1/k) ln(10/7). Solving the ratio: t_exp = 20 × (ln(10/7) / ln(25/21)). Given logs, evaluating this expression yields exactly 40 months. Therefore, correct answer is 0040.

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