Solve the Problem $4.2 \times 10^{9} \mathrm{yr}$ How Long Does It Take a Sample of the \times

Multiple Choice

Solve the problem.
-The half-life of an element is $4.2 \times 10^{9} \mathrm{yr}$ . How long does it take a sample of the element to decay to $\frac{2}{5}$ of its original mass? Use $\mathrm{A}=\mathrm{A}_{0} \frac{1}{2}^{(\mathrm{t} / \mathrm{T}) }$ where $\mathrm{A}_{0}$ is the initial amount, $\mathrm{T}$ is the half-life, and $\mathrm{t}$ is the time. (Express results in scientific notation, rounded to the nearest hundredth.)

A) $9.37 \times 10^{8} \mathrm{yr}$
B) $2.67 \times 10^{9} \mathrm{yr}$
C) $3.94 \times 10^{9} \mathrm{yr}$
D) $5.55 \times 10^{9} \mathrm{yr}$