An isotope decays at a rate of - 0.0049% per year. Find the half life. (show the work)

14,146 years

Step-by-step explanation:

The annual multiplier is (1 - 0.0049%) = 0.999951. We want to find the number of times this needs to be multiplied to make the product 1/2.

0.5 = 0.999951^t

log (0.5) = t·log (0.999951)

log (0.5) / log (0.999951) = t ≈ 14,145.514

The half-life is about 14,146 years.