Answer:
To determine the age of the bones, we can use the formula for exponential decay:
N(t) = N0 * (1/2)^(t/T)
Where:
N(t) = the amount of substance remaining after time t
N0 = the initial amount of substance
t = time that has passed
T = half-life of the substance
Given that 85.2% of carbon-14 has decayed, 14.8% remains. We can express this as a fraction: 0.148.
So, we have:
0.148 = 1 * (1/2)^(t/5750)
Solving for t:
(1/2)^(t/5750) = 0.148
Taking the natural logarithm of both sides:
ln((1/2)^(t/5750)) = ln(0.148)
(t/5750) * ln(1/2) = ln(0.148)
Solving for t:
t = 5750 * ln(0.148) / ln(1/2)
t ≈ 19060 years
Therefore, the bones were approximately 19,060 years old at the time they were discovered.
Step-by-step explanation: