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Situation:A farmer in China discovers a mammalhide that contains 57% of its originalamount of C-14.N = Noe-ktNo inital amount of C-14 (at time=t = 0)N= amount of C-14 at time tk= 0.0001t = time, in yearsFind the age of the mammal hide to the nearestyear.

SituationA Farmer In China Discovers A Mammalhide That Contains 57 Of Its Originalamount Of C14N NoektNo Inital Amount Of C14 At Timet 0N Amount Of C14 At Time class=

Sagot :

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.

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