a) The Lucas numbers La are defined by the difference equation Ln2 = +1 +

L. 20, Lo=2, L=1. Solve the difference equation using z-transform.

b) It is observed that the decrease in the mass of a radioactive substance over a

fixed time is proportional to the mass that was present at the beginning of the

time period (m(t+1) - m(t)=-k m(t)). If the half life of radian is 600 years,

find a formula for its mass as a function of time.