Question

A certain radioactive isotope decays at a rate of 0.3​% annually. Determine the ​half-life of this​ isotope, to the nearest year

Answer 1

This could be rephrased as:

You start with 100 grams of a substance.  One year later you have 70 grams.  What is the half-life?

We need this formula:

half-life = (time * natural log (2)) / natural log (beginning amount / ending amt)

half-life = (1 year * .69315) / natural log (100 / 70)

half-life = (.69315) / 0.35667494396

half-life = 1.9433661145 years

Rounding to nearest year half-life = 2 years

Sourse: https://www.1728.org/halflif2.htm

(See problem 3)