The formula to calculate half-life is:
\[ t_{1/2} = \frac{t \cdot \log(2)}{\log \left( \frac{N_0}{N(t)} \right)} \]
Where:
A half-life is the time it takes for a given substance to deteriorate or lose half of its mass. The term is primarily used in nuclear physics to describe the rate of decay of radioactive substances. It is an important concept in various scientific fields, including chemistry, pharmacology, and environmental science.
Let's assume the following values:
Step 1: Calculate the Half-Life:
\[ t_{1/2} = \frac{10 \cdot \log(2)}{\log \left( \frac{100}{25} \right)} = \frac{10 \cdot 0.693}{\log(4)} = \frac{6.93}{1.386} = 5 \text{ years} \]
Therefore, the half-life is 5 years.
