Final answer:
The population of bacteria can experience exponential growth, doubling in size at consistent intervals.
Step-by-step explanation:
The concept of exponential growth is crucial when studying population dynamics of organisms such as bacteria. The formula Pt = P0 x 2(t/d) reflects this exponential growth, where Pt is the population after time t, P0 is the initial population, and d is the doubling time in hours. If we consider a doubling time of 30 minutes, a single bacterium could theoretically grow to around 281 trillion bacteria in just 24 hours, according to the formula 2n, where n is the number of generations (48 in 24 hours). This kind of growth produces a distinctive J-shaped curve on a graph that plots population size over time.
Looking at practical examples, if we start with an initial population of 1 x 105 cells and a doubling time of 30 minutes, the population would reach 8 x 105 cells after 2 hours, assuming no cell death occurs. This is calculated by recognizing that in 2 hours there would be 4 doubling periods (since 2 hours is equal to 4 periods of 30 minutes each), and thus the cell count would multiply by 24, or 16 times the initial amount.
With a hypothetical scenario of bacterial growth doubling every single minute and starting with a calculated initial number, the jar is expected to be half full exactly one minute before it is full. So, if the jar is full at midnight after 24 hours of doubling, it will be half full at 11:59 PM. It may seem counterintuitive, but this dramatic example underscores the astonishing speed at which exponential growth can occur under ideal conditions.