Writing a Function to Model Exponential Growth A colony contains 1500 bacteria. The population increases at a rate of \( 115 \% \) each hour. If \( x \) represents the number of 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 exponential growth of the bacteria, we can use the formula for exponential growth which typically looks like \( f(x) = P_0(1 + r)^{t} \), where \( P_0 \) is the initial population, \( r \) is the rate of growth (as a decimal), and \( t \) is the time in hours. Since the growth rate is \( 115\% \), we convert it to decimal form which gives us \( 1.15 \). Thus, the correct function is \( f(x) = 1500(1.15)^{x} \). In real-world applications, understanding exponential growth can be crucial. For instance, scientists use these models to predict the spread of bacteria in medical research or the growth of populations in ecology. Accurately predicting how a population evolves over time can inform treatments in healthcare or conservation strategies in environmental science!