The kinetics of radioactive decay is 1st order.
It can be described by: N = N0e-kt
N = concentration of the radioactive substance after time t.
N0 = initial concentration of radioactive substance
k = rate (decay) constant
t = time
The half-life (t1/2) is related to k by: t1/2 = 0.693/k. The half-life time is the time at which the concentration of radioactive is reduced exactly by half.
a. to find the exponential decay mode:
find k from the half-life time: k = 0.693/t1/2 , and then plug in k into the equation: N = N0e-kt.
b. use your equation from (a), and plug in 1000 gram for N0, and 20 years for t.
C. use your equation from (a), and pug in 1000 grams for N0 , and 700 grams for N. Then solve the equation to get t. The unit of t is in years, since the unit of k is per year.
I hope that will help you to solve the problem.