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

Question

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

0

Answers ( No )

    0
    2021-09-19T08:01:18+00:00

    Answer:

    52 Days

    Step-by-step explanation:

    0
    2021-09-19T08:01:37+00:00

    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
     Answer:
     
    D. ≈ 52 days

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