### Home > PC > Chapter 8 > Lesson 8.2.4 > Problem8-129

8-129.

A $100$ gram sample of a radioactive isotope is taken from a protective container. After $4$ hours the sample decays to $85$ garms. What is the half-life of the substance?

Substitute the initial amount of $100$ g for '$a$'. Substitute $85$ for '$y$' and $4$ for '$t$'.

Solve for $h$.

$y = a\left(0.5\right)^{t/h}$

$85 = 100\left(0.5\right)^{4/h}$

$0.85 = \left(0.5\right)^{4/h}$

$\log\left(0.85\right)=\left(4/h\right)\log\left(0.5\right)$