Answer: [tex]f_{(t)}=325(0.87)^{t}[/tex]
Explanation:
If we have an initial amount of a radioactive material or substance, which is [tex]325g[/tex], and we also are told this amount decays [tex]13\%[/tex] each year, this means each year [tex]87\%[/tex] of the substance remains:
[tex]100\%-13\%=87\%=0.87[/tex]
To understand it better:
Year 1: [tex]325(87\%)=325(0.87)[/tex]
Year 2: [tex]325(0.87)(0.87)=325(0.87)^{2}[/tex]
Year 3: [tex]325(0.87)(0.87)(0.87)=325(0.87)^{3}[/tex]
and so on until year [tex]t[/tex]:
Year t: [tex]325(0.87)^{t}[/tex]
Therefore, the function tha best describes this radiation decay situation is:
[tex]f_{(t)}=325(0.87)^{t}[/tex]
