Answer
a. See explanations.
b. $0.1069$ billion years or $106,900,000$ years.
Work Step by Step
a. Assume the model function is
$A=A_0e^{-kt}$
For $t=1.31$ billion years, we have
$A=\frac{A_0}{2}$
Thus
$\frac{A_0}{2}=A_0e^{-1.31k}$
and $k=-\frac{ln(1/2)}{1.31}\approx0.52912$
So we have the model function as $A=A_0e^{-0.52912t}$.
b. Letting $A=0.945A_0$, we have $0.945A_0=A_0e^{-0.52912t}$; thus $t=-\frac{ln(0.945)}{0.52912}\approx0.1069$ billion years or $106,900,000$ years.
