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The question asks whether the statement "A population of bacteria decreases by a factor of \( \frac{1}{8} \) every 24 hours" represents an exponential function.

### Explanation:
An exponential function is defined as a mathematical relationship in which a quantity changes at a constant rate per unit of time. In this case, the population of bacteria is decreasing by a factor of \( \frac{1}{8} \), or 12.5%, every 24 hours. This means the population is multiplied by the same fraction (1/8) after every fixed interval of time (24 hours). 

Mathematically, an exponential decay function is expressed as:
\[
P(t) = P_0 \times \left( \frac{1}{8} \right)^t
\]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( \frac{1}{8} \) is the constant rate of decay,
- \( t \) is the number of time intervals (in this case, 24-hour periods).

Since the decrease follows a constant factor over equal time intervals, **the statement represents an exponential function**.

Thus, the correct answer is:
- **Yes, the statement represents an exponential function.**

Would you like more details on how exponential decay works or need any further clarification?

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Here are 5 related questions to expand your understanding:
1. What is the difference between exponential growth and exponential decay?
2. How do you calculate the half-life of a population using exponential decay?
3. Can exponential functions represent increasing processes? How would you modify the equation?
4. How would the population change if the decay factor was \( \frac{1}{2} \) instead of \( \frac{1}{8} \)?
5. What real-world scenarios besides population decay can be modeled by exponential functions?

**Tip:** Exponential functions are very sensitive to the base of the exponent. Small changes in the decay or growth rate can have large effects over time!

A population of bacteria decreases by a factor of 1/8 every 24 hours. Identify whether the statement represents an exponential function.

Understand how a bacteria population decreases by a factor of 1/8 every 24 hours through exponential decay. Explore key mathematical concepts such as exponential functions and decay rates, and learn how to apply the exponential decay formula P(t) = P_0 × (1/8)^t. Suitable for high school students.

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