A fossil mammoth bone was found to contain 6.25% carbon-14 percent isotope and 93.75% nitrogen-14 daughter isotope. If the half-life of carbon-14 is 5700 years old, how old is the mammoth bone?

The mammoth bone is 22726 years old.

Explanation:

We can find how hold is the mammoth bone using the decay equation:

  (1)

Where:

N(t): is the quantity at time t = 6.25%N₀

N₀: is the initial quantity

λ: is the decay constant

First, we need to find λ:

Now, by solving equation (1) for t we have:

Therefore, the mammoth bone is 22726 years old.

I hope it helps you!

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