i need the explaination and the answer. thank u

Step-by-step explanation:
The americium is represented as 1. Every 432 years it decreases by 50%.
First half-life:
432 years.
[tex]1 \div 2 = 0.50[/tex]
0.50 (1/2) of americium remains after 432 years.
Second half-life:
[tex]432 \times 2 = 864[/tex]
[tex]0.5 \div 2 = 0.25[/tex]
0.25 (1/4) of the americium remains.
Third half-life:
[tex]432 \times 3 = 1296[/tex]
[tex]0.25 \div 2 = 0.125[/tex]
0.125 (1/8) of the americium remains.
Last half-life:
[tex]432 \times 4 = 1728[/tex]
[tex]0.125 \div 2 = 0.0625[/tex]
0.0625 (1/16) of the americium remains.
Option B is correct.