# math

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You have just isolated a new radioactive element. If you can determine its half-life, 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 half-life? (Round your answer to three significant digits.)

• math -

after the theft, there was 1 g left.
If the half-life 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

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