colony contains 1500 bacteria. The population increases at a rate of \( 115 \% \) each hour. If \( x \) represents the number hours elapsed, which function represents the scenario? \( f(x)=1500(1.15)^{x} \) \( f(x)=1500(115)^{x} \) \( f(x)=1500(2.15)^{x} \) \( f(x)=1500(215)^{x} \)

To model the growth of the bacteria, we need to use the exponential growth formula. Since the population increases at a rate of \( 115\% \), this means that each hour the bacteria not only maintain their current number but also add another \( 115\% \). Thus, in one hour, the total population becomes \( 100\% + 115\% = 215\% \) of the original amount, or \( 2.15 \) times the original population. Therefore, the correct function for this growth scenario is \( f(x) = 1500(2.15)^{x} \). Understanding exponential growth is key in biological sciences, economics, and other fields. In this case, after just a few hours, that initial population of 1,500 can balloon to astronomical figures! For instance, after just 3 hours, you would have over 30,000 bacteria. So, next time you’re munching on leftovers, you may want to consider those sneaky microbes multiplying exponentially! When dealing with exponentials, a common mistake is misinterpreting the growth rate. Remember, a \( 115\% \) increase doesn’t mean you multiply by \( 1.15 \) but rather by \( 2.15 \). Additionally, make sure to convert percentage increases properly; confusing them can lead to dramatically different outcomes in calculations. This subtle error often trips up even the best scientists!