General Chemistry 2 Help: Half Life Problem

Question

I don't understand how to ding the problem. If anyone can help, that would be great. Explain in detail please. Thanks.

A radioactive isotope has a half-life of 112 days. What fraction of the isotope remains after 686 days?

a. 0.000057

b. 0.79

c. 0.89

d. 1.00

e. 0.014

Answer 1

log [A] - log [Ao] = - 0.3009 t / half life

log [A] - log [1] = - 0.3009 (686days) / (112 days)

log A  - zero = -1.84

log A   = -1.84

A = 0.014454

your answer is 0.0145 ...   or    1.45/100 ....  or 1/69th