Question

You are trying to determine the half-life of a new radioactive element you have isolated. You start with 1 gram, and 4 days later you determine that it has decayed down to 0.6 grams. What is its half-life? (Round your answer to three significant digits.)

Answer 1

start with general exponential decay function:
\[P = e^{-kt}\]
plug in given point (4,0.6) solve for "k"
\[k = \frac{\ln 0.6}{-4}\]
to determine half-life, set P = 0.5 , solve for "t"
\[t = \frac{4* \ln 0.5}{\ln 0.6}\]