Question

Radioactive isotope #1 has been kept for 1.5 years. Originally, there were 100 grams and now there are 99.39 grams. When will there be 1 gram left?

Answer 1

First we calculate the half-life
half-life = elapsed time * log(2) / log (beginning amt / ending amt)
half-life = 1.5 * 0.3010299957 / log( 1.0061374384 )
half-life = 1.5 * 0.3010299957 / 0.0026573094
half-life = 169.93 years

Now we have to calculate elapsed time for 100 grams to become 1
elapsed time = half-life * log (bgng amt / end amt) / log (2)
elapsed time = 169.93 * log (100/1) / log(2)
elapsed time = 169.93 * 2 / 0.3010299957
elapsed time = 1,129 years

Source:
http://www.1728.org/halflife.htm