Answer:
Option B - 15299
Step-by-step explanation:
Given : A fossilized leaf contains 15% of its normal amount of carbon 14. Use 5600 years as the half-life of carbon 14.
To find : How old is the fossil (to the nearest year)?
Solution :
Let the normal or initial amount of carbon be A,
According to the question,
An exponential function form \(f(t)=ab^t\)
Where, a is the initial i.e, a=A
A fossilized leaf contains 15% of its normal amount of carbon 14.
So, f(t)=15% of A
i.e, \(f(t)=0.15A\)
b is half-life of Carbon-14 b=0.5
and t is the time span or age of the fossil in years.
Substitute all the values in the formula,
\(0.15A=A(0.5)^t\)
\(\frac{0.15A}{A}=(0.5)^t\)
\(0.15=(0.5)^t\)
Taking log both side,
\(\log(0.15)=t\log(0.5)\)
\(t=\frac{\log(0.15)}{\log(0.5)}\)
\(t=2.73\)
For 5600 years the age of the fossil is \(t=2.73\times 5600=15288\)
Therefore, Approximately Option B is correct.
The fossils are 15299 years old.
