Given that carbon-14 `(C_(14))` decays at a constant rate in such a way that it is reduced to 25% in 1244 years. Find the age of a tree in which the carbon is only 6.25% of the original.

Answer

To find the age of a tree in which the carbon-14 is only 6.25% of the original amount, we can follow these steps:

### Step 1: Understand the decay percentages
We know that carbon-14 decays to 25% of its original amount in 1244 years. This means that after 1244 years, only 25% of the original carbon-14 remains.

### Step 2: Determine the decay pattern
If we continue to observe the decay, we can see that:
- After 1244 years, 25% remains.
- After another 1244 years (total 2488 years), the amount will be halved again, which means it will be 12.5% of the original amount.
- After another 1244 years (total 3732 years), the amount will be halved again, which means it will be 6.25% of the original amount.

### Step 3: Calculate the total time for 6.25%
From the above observations, we can conclude:
- The time taken to go from 100% to 25% is 1244 years.
- The time taken to go from 25% to 12.5% is another 1244 years (total 2488 years).
- The time taken to go from 12.5% to 6.25% is another 1244 years (total 3732 years).

Thus, the age of the tree is **3732 years**.

### Final Answer:
The age of the tree is **3732 years**.

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