### Home > PC > Chapter 8 > Lesson 8.2.4 > Problem 8-129

8-129.

A 100 gram sample of a radioactive isotope is taken from a protective container. After four hours the sample decays to 85 grams. What is the half-life of the substance? Homework Help ✎

Substitute the initial amount 100 for '*a*'. Substitute 85 for '*y*' and 4 for '*t*'.

Solve for *k*.

Since we want to find how long it takes for half to decay, solve: 1 = 2*e*^{−0.0406}^{t}

This indicates an amount of 2 was reduced to 1.

*y* = *ae ^{kt}*

85 = 100*e*^{4}^{k}

*k* = −0.0406

*t* = 17.06 hours