A sample contains an isotope of half-life t _{1/2 .}
a. Show that the fraction f of nuclei in the sample that remain undecayed after a time t is given by the equation:

f = (1/2)ⁿ where n = 1/t _1/2

b. Calculate the fraction f after each of the following times:

i. t _1/2

ii.  2t _1/2

iii. 2.5t _1/2

iv. 8.3t _1/2