Answer:
7340 years
Step-by-step explanation:
A student in Greece discovers a pottery bowl that contains 48% of the original C-14.
Decay of C - 14 is represented by the expression given
N = [tex]N_{0}e^{-kt}[/tex]
where, [tex]N_{0}[/tex] = initial quantity of C-14 = 100% = 1
N = quantity of C-14 after t years = 48% = 0.48
k = 0.0001
and t = time in years.
We have to find the age of the bowl.
0.48 = [tex]1(e)^{(-0.001)(t)}[/tex]
By taking natural logarithm
ln ( 0.48 ) = ln [tex]e^{(-0.0001)(t)}[/tex]
-0.73397 = -0.0001t [ since ln e = 1 ]
t = [tex]\frac{0.73397}{0.0001}[/tex]
t = 7340 years
Age of the pottery of bowl is 7340 years.
