A radioactive isotope has a half life of 75.3 minutes. How long will it take for the radiation from a 325 pCi sample to decrease to 162 pCi?

Let n be the number of half-lives.

162 = 325 × (1/2)ⁿ
(0.5)ⁿ = 162/325
n log(0.5) = log(162/325)
n = log(162/325) / log(0.5)

Time taken = 75.3 × [log(162/325) / log(0.5)] min = 75.6 min

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OR:
Rate constant, k = ln(2)/t½ = ln(2)/75.3 /min

ln(A) = -kt + ln(Aₒ)
ln(162) = -[ln(2)/75.3]t + ln(325)
[ln(2)/75.3]t = ln(325) - ln(162)
Time taken, t = 75.3 × [ln(325) - ln(162)] / ln(2) min = 75.6 min