How long will it take for 750 mg of a sample of radium-225, which has a half-life of about 15 days, to decay to 68 mg? a. ≈ 50 days b. ≈ 54 days c. ≈ 48 days d. ≈ 52 days

For this case we have an equation of the form:
 y = A (b) ^ t
 Where,
 A: initial amount
 b: decrease rate
 t: time
 Substituting values:
 y = 750 (0.5) ^ ((1/15) * t)
 The number of days to reach 68 mg is:
 68 = 750 (0.5) ^ ((1/15) * t)
 Clearing t:
 (0.5) ^ ((1/15) * t) = (68/750)
 log0.5 ((0.5) ^ ((1/15) * t)) = log0.5 (68/750)
 (1/15) * t = log0.5 (68/750)
 t = 15 * log0.5 (68/750)
 t = 51.94
 Rounding:
 t = 52 days
 
 D. ≈ 52 days