1. **State the problem:** We are given data showing the number of bacteria at different times and need to find an equation that models this data. 2. **Identify the pattern:** The bacteria count halves every second: from 192 to 96, then 48, 24, and 12. 3. **Use the exponential decay formula:** $$y = y_0 \times r^x$$ where $y_0$ is the initial amount, $r$ is the decay rate, and $x$ is time. 4. **Plug in the values:** Initial amount $y_0 = 192$, decay rate $r = 0.5$ (since it halves every second). 5. **Write the function:** $$y = 192 \times (0.5)^x$$ 6. **Explain:** This means the bacteria count halves each second, starting from 192 at time 0. 7. **Final answer:** $$\boxed{y = 192 \times (0.5)^x}$$