Half-life of substance

Question

Suppose 128 ounces of a substance exponentially decays to 28 ounces in 6 hours. What is the half-life?

Answer 1

28 = 128(0.5)^6/h               divide both sides by 128

0.21875 = (0.5)^6/h             take natural log of both sides

ln 0.21875 = (6/h) ln 0.5    calculate

-1.5198 ≈ (t/h) (-0.6931)   divide both sides by -0.6931

2.19 ≈ 6/h                         take reciprocal 

0.456 ≅ h/6                      multiply both sides by 6

2.736 ≈ h

 

The half-life is approximately 2.7 hours.