Final answer:
To determine the initial bacteria population with a doubling time of 23 minutes and a population of 42,414 after 48 minutes, we calculated that there were 2 doublings, resulting in an estimated initial population of approximately 10,603 bacteria.
Step-by-step explanation:
The student's question relates to determining the initial population of a bacteria colony given its doubling time and population size after a certain period. Since the doubling period of the bacteria is 23 minutes and the population reaches 42,414 after 48 minutes, we can calculate the initial population.
To find the number of doublings that occurred within 48 minutes, we divide 48 by 23 minutes per doubling, which gives us approximately 2.087 doublings. However, because bacteria can only double in whole numbers, we assume that there were exactly 2 doublings in the 48-minute window.
Knowing this, we can reverse the growth process. If the bacteria doubled twice to reach 42,414, we divide 42,414 by 2, then divide the result by 2 again. This gives us:
- First division: 42,414 / 2 = 21,207
- Second division: 21,207 / 2 = 10,603.5
The initial population of the bacteria colony was approximately 10,603 bacteria.