A scientist is studying the growth of a bacterial culture. The culture initially contains 500 bacteria and grows by 12% per hour. How many bacteria will be present after 5 hours?
["Title: How a Bacterial Culture Grows: A Scientific Look at Exponential Growth", "Understanding bacterial growth is essential in fields ranging from microbiology to medicine and food safety. A key example involves exponential growth, where organisms multiply rapidly under favorable conditions. In this article, we explore the case of a scientist studying a bacterial culture that starts with 500 bacteria and grows at a steady rate of 12% per hour—providing insights into how often such cultures expand over time.", "### The Science Behind Bacterial Growth", "Bacterial growth typically follows an exponential pattern when nutrients and environmental conditions are optimal. This means the population increases by a consistent percentage during each time interval, rather than adding a fixed number. The formula used to model this growth is:", "[\nN(t) = N_0 \ imes (1 + r)^t\n]", "Where:\n- ( N(t) ) = number of bacteria at time ( t )\n- ( N_0 ) = initial number of bacteria\n- ( r ) = growth rate per time unit (as a decimal)\n- ( t ) = time in hours", "### Applying the Formula to the Given Scenario", "In our case:\n- Initial population ( N_0 = 500 )\n- Growth rate ( r = 12% = 0.12 )\n- Time ( t = 5 ) hours", "Plugging these values into the formula:", "[\nN(5) = 500 \ imes (1 + 0.12)^5\n]", "First, calculate ( 1 + 0.12 = 1.12 ). Then raise it to the 5th power:", "[\n1.12^5 \approx 1.7623\n]", "Now multiply by the initial count:", "[\nN(5) = 500 \ imes 1.7623 \approx 881.15\n]", "Since the number of bacteria must be a whole number, we round to the nearest bacterium:", "Approximately 881 bacteria", "### Conclusion", "After 5 hours, the bacterial culture—starting with 500 bacteria and growing at 12% per hour—will contain roughly 881 bacteria. This exponential growth demonstrates how rapidly microorganisms can expand under ideal conditions. For scientists and healthcare professionals, modeling such growth helps in predicting infections, designing treatments, and ensuring laboratory safety.", "Understanding the math behind microbial expansion remains critical in advancing research and protecting public health. Next time you encounter microbial studies, remember that behind every growth curve lies a precise calculation—one that scientists rely on daily."]
