ANSWER
86 grams
EXPLANATION
We have 344 grams of radioactive cobalt.
To find how many years will be left after 10 years if its half life is 5 yrears.
To do this, we apply the formula for exponential decay:
[tex]\begin{gathered} A=A_o\cdot e^{\frac{^{-0.693\cdot t}}{T}} \\ \text{where A}_o=initial\text{ amount} \\ t\text{ = number of years} \\ T=\text{half life} \end{gathered}[/tex]Therefore, we have that:
A - 344 grams
t = 10 years
T = 5 years
[tex]\begin{gathered} A=344\cdot e^{\frac{-0.683\cdot10}{5}} \\ A=344\cdot e^{-1.386} \\ A=344\cdot0.25 \\ A=86\text{ grams} \end{gathered}[/tex]That is the amount that will be left after 10 years.
