Step-by-step explanation:
a.
Initial mass of the isotope = x
Time taken by the sample to decay its mass by 41% = t
Formula used :
where,
= initial mass of isotope = x
N = mass of the parent isotope left after the time, (t) = 59% of x = 0.59x
= half life of the isotope = 4.5 billion years
= rate constant
Now put all the given values in this formula, we get
t = 3.4 billion years
The age a rock is 3.4 billion years.
b.
Initial mass of the isotope = x
Time taken by the sample to decay its mass by 35%= t
Formula used :
where,
= initial mass of isotope = x
N = mass of the parent isotope left after the time, (t) = 65% of x = 0.65x
= half life of the isotope = 4.5 billion years
= rate constant
Now put all the given values in this formula, we get
t = 2.8 billion years
The age a rock is 2.8 billion years.