Choose the One Alternative That Best Completes the Statement or Answers

Multiple Choice

Choose the one alternative that best completes the statement or answers the question.
-The half-life of an element is $5.4 \times 10 ^ { 9 } \mathrm { yr }$ . How long does it take a sample of the element to decay to $\frac { 2 } { 3 }$ of its original mass? Use $A = A _ { 0 } ( 0.5 ) ^ { ( t / T ) }$ where $A _ { 0 }$ 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) $1.52 \times 10 ^ { 9 } \mathrm { yr }$
B) $8.39 \times 10 ^ { 9 } \mathrm { yr }$
C) $1.55 \times 10 ^ { 9 } \mathrm { yr }$
D) $3.16 \times 10 ^ { 9 } \mathrm { yr }$