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Sally
 5 years ago
This is the last question I have and need help w/:
Given exponential decay rate of 0.9%, how old is an animal bone that has lost 40% of its carbon14?
Sally
 5 years ago
This is the last question I have and need help w/: Given exponential decay rate of 0.9%, how old is an animal bone that has lost 40% of its carbon14?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Since you started with 100% and after certain time t you loss 40% which means you're left with 60%, so your initial value is 100% and your final value is 60%, your decay rate k=0.9%, convert all these percentages to decimal form: \[N(t)=N_{0}e^{kt}\rightarrow N(t)=.6, N_{0}=1, k=.009\] \[.6=1*e^{.009t}\rightarrow .6=e^{.009t}\rightarrow \ln(.6)=\ln(e^{.009t})\] \[\ln(.6)=(.009t)\ln(e)\rightarrow \ln(e)=1, so \rightarrow \ln(.6)=.009t\] \[\frac{\ln(.6)}{.009}=t\]
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