Question

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Answer 1

About 2614 years.

Explanation:

We are given k, and the information that N/N0 = 0.77, so the C-14 function becomes:

`N=N_0\cdot e^(-kt) \\0.77N_0 = N_0\cdot e^(-kt)\\0.77 = e^(-0.0001 t)`

and we can solve for t:

`0.77 = e^(-0.0001 t)\\\ln0.77 = \ln e^(-0.0001 t)\\\ln 0.77 = -0.0001 t\implies\\t = -(\ln0.77)/(0.0001)=2613.65\approx 2614\,\,\,\mbox{years}`

The estimated age of the bird skeleton is 2614 years.