Explanation:
it means every 2 years half of the mass left 2 years ago is gone.
6 years means 3 such 2-year periods.
so, after the first 2 years 1/2 of 20g is left.
after the next 2 years half of that remaining mass is gone.
and after the 3rd 2-year period half of that remaining mass is gone.
that means
(((20/2) / 2) / 2) = 20/(2×2×2) = 20/2³ = 20/8 = 2.5g
after 6 years 2.5g are left of the sample.
FYI
in general that gives us the function
mass(y) = 20×(1/2)^(y/2)
with y being the number of years.
we divide the exponent of the decay factor by 2, so that it increases by 1 only every 2 years (we cut the remaining mass fully in half only every 2 years). so, e.g. 6 years give us the exponent 6/2 = 3. just what we needed.
but this gives us also the decay result for fractions of years (e.g. after 1.5 years). after all, decay does not just happen at the end of a half-life period. it happens continuously with time.
