Carbon-containing compounds in living organisms maintain an equilibrium with `""^(14)C` in the atmosphere. The activity associated with C in the equilibrium is 15 disintegrations/minute/gram of carbon (`t_(1//2) " of " ""^(14)C=5730` years). An old tree, found in an burial, was subjected to radioactive dating. The decay rate associated with its `""^(14)C` content is 10 disintegrations/minute/gram of C. Find the time elapsed since the tree was cut down.

Explanation

To solve the problem of determining the time elapsed since the tree was cut down using radioactive dating, we can follow these steps:

### Step 1: Understand the Given Information
- The activity of `^(14)C` in equilibrium with living organisms is 15 disintegrations/minute/gram of carbon.
- The activity of `^(14)C` in the old tree is 10 disintegrations/minute/gram of carbon.
- The half-life of `^(14)C` is 5730 years.

### Step 2: Calculate the Decay Constant (λ)
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