The C-14 content of an ancient piece of wood was found to have three tenths of that in living trees. How old is that piece of wood? (log 3= 0.4771, log 7 = 0.8540 , Half-life of C-14 = 5730 years )

Explanation

To determine the age of the ancient piece of wood based on the C-14 content, we can use the formula for radioactive decay. The amount of C-14 remaining can be expressed in terms of its half-life.

### Step-by-Step Solution:

1. **Understanding the Problem**:
The C-14 content of the ancient wood is three tenths (0.3) of that in living trees. This means that if we denote the initial amount of C-14 in living trees as \( N_0 \), the amount remaining in the ancient wood \( N \) is:
\[
N = 0.3 N_0
...