The half-life of a radioactive isotope is 82 days. To the nearest hundredth of a day, how long will it take ..

Question

...a 350 g sample to decay to 110 g?

Answer 1

135.59 days

.5 = (D)^82 D= decay factor = .9915

110 = 350 (.9915)^t where t is the time for 350g to decay to 110g
log (110/350) = t x log(.9915)

Answer 2

M = Mo*e^(-kt)
When t = 82 M = ½Mo
Therefore
½ = e^(-82k)
ie e^(82k) = 2
So e^k = 2^(1/82)

Therefore
M = Mo * 2^(-t/82)

So 110 = 350 * 2^(-t/82)
2^(-t/82) = 110/350
2^(t/82) = 350/110
Taking logs
t/82 * log 2 = log350 - log110
So t = 82*(log350 - log110)/log2
≈ 136.93 days

Answer 3

82 * log base 2 of 350/110

that log can be computed as natural log of 350/110 divided by natural log of 2. (or decimal logs)

you can compute logs using a Windows Calculator (Start/programs/Accesories) in Science mode.