Answer to Question #257905 in Algebra for Joel

Question

A radioactive Isotope Gallium – 67, used in diagnosing malignant tumor, has a biological half – life of 46.5 hours. If we start with 100mg of the isotope, how many milligrams will be left after 24 hours

Answer 1

Use the half-life decay model as follows:

$A = A _{0}(\frac{1}{2})\\^\frac{-t}{h} \\= A _{0}2^\frac{-t}{h}$

Using $A _{0} = 100$ and $h = 46.5$, we obtain:

$100(2^\frac{-t}{46.5})$

After 24 hours:

$100(2\\^\frac{-24}{46.5})\\= 69.9245 \ milligrams$