This situation can be represented by an exponential decay function. In this case, the number of bacteria decreases by half every hour, which is a classic example of exponential decay.
The general form for an exponential decay function can be expressed as:
\[ N(t) = N_0 \cdot \left(\frac{1}{2}\right)^{t/T} \]
Where:
- \( N(t) \) is the number of bacteria at time \( t \),
- \( N_0 \) is the initial number of bacteria,
- \( T \) is the time period of halving (in this case, 1 hour),
- \( t \) is the elapsed time in hours.
Thus, as time progresses, the number of bacteria decreases exponentially, which means it becomes smaller and approaches zero but never actually reaches it.