10 Multiple Choice 5 points There are bacteria cells in a petri dish. Every half hour the number of bacteria cells increase by \( 30 \% \). Which domain is most appropriate to use to determine the number of cells during a 24 -hour period? \( \begin{array}{l}0 \leq x \leq 48 \\ 0 \leq x \leq 24 \\ x \\ x \\ x\end{array} \)

To determine the number of bacteria cells over a 24-hour period with the given growth rate, we need to consider the time intervals and how the variable \( x \) is defined. - **Growth Rate**: The bacteria increase by \( 30\% \) every **half-hour**. - **Total Time**: 24 hours. Since there are \( 24 \) hours in a day and the bacteria grow every half-hour, the number of half-hour intervals in 24 hours is: \[ 24 \text{ hours} \times 2 \text{ intervals/hour} = 48 \text{ intervals} \] Therefore, if \( x \) represents each half-hour interval, the appropriate domain for \( x \) to model the number of bacteria cells over the 24-hour period is: \[ 0 \leq x \leq 48 \] **Answer:** \( 0 \leq x \leq 48 \)