Final answer:
The function y = 100(1.20)^x models exponential growth, where 100 is the initial quantity of bacteria, 1.20 is the growth factor, and x represents the number of time intervals. The final number of bacteria after growth is represented by y.
Step-by-step explanation:
The question pertains to an exponential growth function and its interpretation regarding the growth of a bacteria colony. The function in question is y = 100(1.20)^x.
The correct statements are:
- B) This is an exponential function. The base 1.20 raised to the power of x indicates that the growth of the bacteria colony is proportional to its current size, meaning the larger the colony becomes, the faster it will grow. This aligns with the understanding of exponential growth in biology.
- D) 100 is the initial number of bacteria. In the function, 100 represents the initial quantity of the bacteria at the start of observation, before any growth has occurred.
- E) y equals the final number of bacteria. In this function, y represents the total number of bacteria at a given time, after growth has been accounted for according to the exponential formula.
While A) and C) present incorrect statements:
- A) x is not the growth factor; it is the number of time intervals over which the colony grows.
- C) 1.20 is not the number of time intervals, but rather the growth factor which indicates that with every time interval, the number of bacteria increases by a factor of 1.20.
It is key to understanding that in the context of a growing bacterial population, the concept of exponential growth implies that the number of organisms added in each reproductive generation is accelerating. As the bacteria divide and the population increases, they lead to their original amount over time, demonstrating the power of exponential increase in ideal conditions.