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

Answer:

D. ≈ 52 days