6. The number of bacteria in a petri dish decreases by half each hour. If the population of bacteria starts at 12,000 , which of the following exponential equation \( 12000=a\left(\frac{3}{2}\right)^{x} \) \( y=12000\left(\frac{1}{4}\right)^{x} \)

To determine the correct equation for the bacteria population that halves every hour, we start with the initial population of 12,000. An exponential decay model typically takes the form \( y = a \left( \frac{1}{b} \right)^{x} \), where \( a \) is the initial population and \( b \) is the base representing the decay factor. Here, since the bacteria population is halving, we use a decay factor of 2. Thus, the appropriate equation can be expressed as \( y = 12000 \left( \frac{1}{2} \right)^{x} \). However, among the provided options, the equation should reflect the halving of the population consistently in such a way that at \( x = 1 \), the population is half of 12,000, yielding 6,000. Therefore, neither of the provided options is correctly structured for this scenario. In summary, the exponential decay of bacteria is best modeled by \( y = 12000 \left( \frac{1}{2} \right)^{x} \).