The fraction of a radioactive isotope remaining at time t is (1/2)^t/t1/2 where t1/2 is the half-life. if the half-life of carbon−14 is 5,730 yr, what fraction of carbon−14 in a piece of charcoal remains after
(a) 14.0 yr?
(b) 1.900 × 10^4 yr? × 10 (enter your answer in scientific notation.)
(c) 1. × 10^5 yr? × 10 (enter your answer in scientific notation.)

a) fraction of carbon−14 in a piece of charcoal remains after 14.0 years.

b) fraction of carbon−14 in a piece of charcoal remains after  

c) fraction of carbon−14 in a piece of charcoal remains after  .

Explanation:

The fraction of a radioactive isotope remaining at time t is given by:

Taking log both sides:

[A] =  fraction at given time t

= half life of the carbon−14 =5,730 years

a)When , t = 14 years

b)When , t =

c)When , t =