Final answer:
The function P(t) = 12 \* 2^(t/9) is a correct representation of exponential growth for a bacteria population that doubles every 9 hours starting with a population of 12, which aligns with biological observations of bacteria reproduction.
Step-by-step explanation:
The statement that a bacteria population doubles every 9:00 AM and the population is 12 bacteria, modeled by the function P(t) = 12 \* 2^(t/9), is True. This formula represents exponential growth, where t is the number of hours after the initial observation and 2^(t/9) shows the number of times the bacteria population has doubled after t hours. For example, after 9 hours (one full cycle), the population would be 12 \* 2^(1), which equals 24 bacteria, showing that the population has indeed doubled.
Exponential growth is characterized by a constant doubling time and results in a J-shaped growth curve when population size is plotted over time. This is commonly observed in bacteria that reproduce through prokaryotic fission, which in an ideal environment with plentiful nutrients, can result in dramatic increases in population size within a matter of hours. The model given aligns with this concept by indicating that the initial count of bacteria is 12, and it doubles every 9 hours.