Answer: 2.223 billion years old
Step-by-step explanation:
since 71 percent of the rock is remaining, the half life hasn't been reached yet. Hence, we know uranium isn't 4.5 billion years old yet. However, every-time 4.5 billions years pass, the rock get smaller by 2 times(a scale factor of 1/2). Hence, you can express that in a log equation:
[tex]\log_{2}(100/(percent of rock remaining))=[/tex] Fraction of 4.5 billions years of time passed
[tex]\log_{2}(100/50)=1[/tex] ==> 100% of 4.5 billion years passed. When 50% of rock remains, 4.5 billion years have passed.
[tex]\log_{2}(100/100)[/tex] =
[tex]\log_{2}(1)=0[/tex] ==> 0% of 4.5 billion years passed. When the rock hasn't decayed at all yet, that means that it is 0 years old.
[tex]\log_{2}(100/71)=0.494[/tex] ==> 49.4 % of 4.5 billion years passed
0.494*4.5 billion =2.223 billion years passed
2.223 billion years old