Bacteria in a bottle are tripling every minute. If the number of bacteria in the bottle at \( 3: 30 \) p.m. is. 1, how many bacteria are in the bottle at \( 3: 48 \) p.m.? Answer How to enter your answer (opens in new window)

From \( 3:30 \) p.m. to \( 3:48 \) p.m. is \( 18 \) minutes in total. Since the bacteria triple every minute, we can calculate the number of bacteria at \( 3:48 \) p.m. by using the formula \( 1 \cdot 3^{n} \), where \( n \) is the number of minutes. In this case, \( n = 18 \). Thus, the number of bacteria is \( 1 \cdot 3^{18} = 387420489 \). So, there are \( 387420489 \) bacteria in the bottle at \( 3:48 \) p.m. A fun fact: Bacterial growth can lead to astonishing numbers in absolutely no time! In just 1 hour, starting with a single bacterium, you could have over 3.87 billion! This rapid growth underpins the basis of many biological processes, from digestion to fermentation, and why we need to be careful with food storage. It's amazing how such tiny organisms can impact our daily lives, isn't it? If this seems a bit overwhelming, remember the trick of breaking down the problem! Instead of calculating for all 18 minutes at once, think about smaller intervals. For example, compute the number of bacteria after each minute and observe the pattern: \( 1, 3, 9, 27, \) and so on! This makes it easier to visualize and can help avoid mistakes with larger numbers. Math can be less intimidating when approached in smaller bites!