Half-life problem help!?

A)
Originally, there are 300 atoms of element A, and no atom of element Z.
1 atom of element A decays to form 1 atom of element Z.

After 10 years :
Number of atoms of element A left = 9
Number of atoms of element Z present = 300 - 9 = 291


B)
Let n be the number of half-lives in 10 years.

Fractions of atoms of element A left after 10 years :
(1/2)ⁿ = 9/300
(0.5)ⁿ = 0.03
log(0.5ⁿ) = log(0.03)
n log(0.5) = log(0.03)
n = log(0.03) / log(0.5)

Half-life = 10/n years = 10/ [log(0.03) / log(0.5)] = 1.98 years

If one A decomposes in one Z, then you have 291 Z (300 - 9).
For the half life, use the law of activity A(n)=A°/2^n
where A(n) is the activity after n periods (or half lives) have occurred, A° the initial activity.
Activity can be simplified and you can use the quantity of matter as a pretty good approximation.
A(n)=A°/2^n
2^n = A°/A(n)
n.ln(2) = ln(A°/A(n))
n = ln(A°/A(n)) / ln(2)
n = ln(300/9)/ln(2)
n = 5.06
Meaning that 5.06 half lives have passed in ten years.
So lamdba = 10/5.06 = 1.98 years.