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Situation:A farmer in China discovers a mammalhide that contains 42% of its originalamount of C-14.N = Noe-ktNoinital amount of C-14 (at timet = 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 42 of its originalamount of C14N NoektNoinital amount of C14 at timet 0N amount of C14 at time t class=

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Solution

Given that;

[tex]\begin{gathered} N=N_0e^{-kt} \\ \\ \text{ Given that } \\ \\ N=\frac{42}{100}N_0 \\ \\ k=0.0001 \end{gathered}[/tex]

we need to find t,

=>

[tex]\begin{gathered} \frac{42}{100}N_0=N_0e^{-0.0001t} \\ \\ \Rightarrow\frac{42}{100}=e^{-0.0001t} \\ \\ \Rightarrow\ln(\frac{42}{100})=-0.0001t \\ \\ \Rightarrow t=\frac{\ln(\frac{42}{100})}{-0.0001} \\ \\ \Rightarrow t=8675 \end{gathered}[/tex]

The answer is 8675 years

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