Explanation:
a) Given: t1/2 = ln(0.5) / k ( this is NATURAL ln...NOT base 10 LOG)
then k = ln(0.5) / ( t1/2) and t 1/2 is given as 1620 yrs
k = ln(0.5) / 1620 = - 4.279 x 10^-4
b) New = n e^(kt) n = 20 g t = 5000 k (given above)
New = 20 e^(-4.279 x 10^-4 * 5000) = 2.23 g left
c) 1/4 = e^(kt)
1/4 = e^( 4.279x 10^-4 * t) solve for t years
t = 3240 years <==== which makes sense
say you started with 10 g
after one half life you would have 5
one more half life you would have 2.5
so two half lives and you have 1/4 as much
two half lives = 1620 x 2 = 3240 years