CPM Homework Help : PC3 Problem 6-112

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

Step 1:

Step 2:

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

Step 3:

Solve for $h$ .

Step 4:

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

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

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

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