The amount of a sample remaining after t days is given by the equation p (t) = a (1 / 2) ^ t / h, where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 60% of its original amount of Fermium-257. The half-life of Fermium-257 is about 100 days. About how old is the sample?

A. 52 days

B. 60 days

C. 74 days

D. 136 days

Question

Mathematics

Leonidas Barrett

12 January, 17:36

The amount of a sample remaining after t days is given by the equation p (t) = a (1 / 2) ^ t / h, where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 60% of its original amount of Fermium-257. The half-life of Fermium-257 is about 100 days. About how old is the sample?

A. 52 days

B. 60 days

C. 74 days

D. 136 days

+3

Answers (1)

Know the Answer?

Jonathan Rubio · Answer 1

Assume the original mass,

a=100, then we know

p (t) = 0.6*100=60,

h=100,

Substitute into equation and solve for t.

60=100 * (1/2) ^ (t/100)

divide by 100

0.6 = (1/2) ^ (t/100)

take log on both sides

log (0.6) = (t/100) log (1/2)

divide each side by log (1/2)

t/100=log (0.6) / log (0.5)

t=100log (0.6) / log (0.5)

=100 (-0.5108) / (-0.6931)

=73.70 days, approximately