math
posted by Roseanne on .
You have just isolated a new radioactive element. If you can determine its halflife, you will win the Nobel Prize in physics. You purify a sample of 2 grams. One of your colleagues steals half of it, and eight days later you find that 0.1 gram of the radioactive material is still left. What is the halflife? (Round your answer to three significant digits.)

after the theft, there was 1 g left.
If the halflife is n days, then the fraction left after t days is
(1/2)^(t/n)
so, solve this for n:
0.1 = (1/2)^(8/n)
ln 0.1 = (8/n) ln 0.5
ln .1/ln .5 = 8/n
n = 8 * ln .5/ln .1
n = 2.4 days