Which equation determines the percent of an initial amount of the isotope remaining after t years?

amount after  0  years  =  N

amount after  5.27 years  =  (1/2)N

amount after  2 * 5.27 years  =  (1/2)(1/2)N

amount after  3 * 5.27 years  =  (1/2)(1/2)(1/2)N  =  (1/2)³N

amount after  x * 5.27 years  =  (1/2)^xN

 

x * 5.27  =  t

x  =  t / 5.27

 

amount after  t  years  =  (1/2)^{t / 5.27}N

amount after  t  years  =  \((\frac12)^{\frac{t}{5.27}}N\)

 

\(A=(\frac12)^{\frac{t}{5.27}}N\\ A=N(\frac12)^{\frac{t}{5.27}}\)

 

If the initial amount is  100, then...

 

\( A=100(\frac12)^{\frac{t}{5.27}}\)