The Half-Life of an Element Is $4.5 \times 10 ^ { 11 } \text { yr. }$

Multiple Choice

The half-life of an element is $4.5 \times 10 ^ { 11 } \text { yr. }$
How long does it take a sample of the element to decay to $\frac { 2 } { 3 }$ of its original mass? Use $\mathrm { A } = \mathrm { A } _ { 0 } ( 0.5 ) ^ { ( \mathrm { t } / \mathrm { T } ) }$ where $\mathrm { A } 0$ is the initial amount, T is the half-life, and t is the time. (Express results in scientific notation, rounded to the nearest hundredth.)

A) $2.63 \times 10 ^ { 11 } \mathrm { yr }$
B) $5.83 \times 10 ^ { 11 } \mathrm { yr }$
C) $1.29 \times 10 ^ { 11 } \mathrm { yr }$
D) $1.26 \times 10 ^ { 11 } \mathrm { yr }$