Given:
A farmer in China discovers a mammal hide that contains 57% of its original
amount of C-14.
The given formula is
[tex]N=N_0e^{-kt}[/tex]
where k =0.0001.
Required:
We need to find the age of the mammal hide.
Explanation:
The number of mammals hiding is 57% of the original.
[tex]N_t=57\text{ \%}[/tex]
We get
[tex]\text{ We get }N_0=1\text{ and }N=57.[/tex][tex]Substitute\text{ }N=0.57,\text{ }N_0=1\text{ and k=0.0001 in the equation }N=N_0e^{-kt}\text{ to find t value.}[/tex][tex]0.57=1\times e^{-0.0001t}[/tex][tex]0.57=e^{-0.0001t}[/tex]
Take a natural log on both sides of the equation.
[tex]In\text{ }0.57=Ine^{-0.0001t}[/tex][tex]In\text{ }0.57=-0.0001\times t[/tex][tex]\frac{-In0.57}{0.0001}=t[/tex][tex]5621.18=t[/tex][tex]t=5621years.[/tex]
Final answer:
The age of the mammal hide is 5621 years.
