The amount of a decaying substance with half life τ that remains after a time t, if the initial amount of that substance is A_0, is given by the formula:
[tex]A(t)=A_0\cdot2^{-\frac{t}{\tau}^{}}[/tex]
If the half life of that substance is 12 days, and the initial amount of that substance is 4.5 grams, then A_0=4.5 and τ=12. Substitute those values as well as t=20 to find the remaining amount after 20 days:
[tex]\begin{gathered} A(t)=4.5\times2^{-\frac{t}{12}} \\ \Rightarrow A(20)=4.5\times2^{-\frac{20}{12}} \\ =4.5\times2^{-\frac{5}{3}} \\ =4.5\times0.3149\ldots \\ =1.4174\ldots \end{gathered}[/tex]
To the nearest tenth of a gram, the remaining amount after 20 days, is:
[tex]1.4\text{ grams}[/tex]
