Question

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? 52 days 60 days 74 days 136 days

Answer 1

74 days

Explanation:

The proportion left after d days is ...

p = (1/2)^(d/100)

When that proportion is 60%, we have ...

.60 = .50^(d/100)

log(.60) = (d/100)log(.50) . . . . . take logarithms

100·log(.60)/log(.50) = d ≈ 73.697 ≈ 74 . . . days