The amount of carbon-14 remaining in a sample that weighs B is given by $X ( t ) = B ( 0.999879 ) ^ { t }$
where t is time in years. If tests on a fossilized skull reveal that 99.92% of the carbon-14 has decayed, how old is the skull
Select the correct answer rounded to the nearest integer.

A)58,929 years old
B) 2,629 years old
C) 1,985 years old
D) 0 years old
E) 23,234 years old

Question

The amount of carbon-14 remaining in a sample that weighs B is given by $X ( t ) = B ( 0.999879 ) ^ { t }$ 
where t is time in years. If tests on a fossilized skull reveal that 99.92% of the carbon-14 has decayed, how old is the skull  
Select the correct answer rounded to the nearest integer.
 
A)58,929 years old
B) 2,629 years old
C) 1,985 years old
D) 0 years old
E) 23,234 years old

Quizplus · Accepted Answer

To find the age of the skull, we need to solve for $t$ in the equation $X(t) = B(0.999879)^t$. Given that 99.92% of the carbon-14 has decayed, this means that 0.08% remains. Thus, we set $X(t) = 0.0008B$ and solve for $t$. Rearranging the equation and solving for $t$ involves logarithms, leading to the correct answer after calculations.

The Amount of Carbon-14 Remaining in a Sample That Weighs X(t)=B(0.999879)tX ( t ) = B ( 0.999879 ) ^ { t }X(t)=B(0.999879)t

The Amount of Carbon-14 Remaining in a Sample That Weighs $X ( t ) = B ( 0.999879 ) ^ { t }$