# A radioactive substance has a half life of 120 years. Presently, there are 60 grams of the substance. When were 600 grams present?

Nov 24, 2017

399

#### Explanation:

Using the formula $A \left(F I n a l\right) = A \left(I n i t i a l\right) \cdot {\left(\frac{1}{2}\right)}^{\frac{t}{h}}$, you can input your information from the questions into there.
$60 = 600 \cdot {\left(\frac{1}{2}\right)}^{\frac{t}{120}}$
$0.1 = {\left(\frac{1}{2}\right)}^{\frac{t}{120}}$
$\frac{t}{120} = {\log}_{\frac{1}{2}} 0.1$
$\frac{t}{120} = 3.21928 \ldots$
$t = 398.63137 \ldots = 399$