Initially 100 milligrams of a radioactive substance was present. after 8 hours the mass had decreased by 6%. if the rate of decay is proportional to the amount of the substance present at time t, determine the half-life of the radioactive substance.

  89.6 hours

Step-by-step explanation:

Each hour, the initial quantity is multiplied by (1 -0.06)^(1/8), so after t hours, the multiplier is 0.94^(t/8). We want to find the value of t that makes this multiplier equal to 1/2.

  0.5 = 0.94^(t/8)

  log(0.5) = (t/8)log(0.94) . . . . . . . . take logs

  t = 8·log(0.5)/log(0.94) ≈ 89.6 . . . divide by the coefficient of t

The half-life of the substance is 89.6 hours.

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