Final answer:
The bacteria population decreases by more from day 1 to day 3 than from days 4 to 6 due to the nature of percentage decrease in a population over time. This is a direct consequence of exponential decay, where the amount of the decrease gets smaller as the population shrinks.
Step-by-step explanation:
The decrease in the number of bacteria over a period of days can be analyzed using basic principles of percentage decrease, which fall under the subject of exponential decay in mathematics. To solve this problem, we will calculate the decrease in bacteria population from day 1 to day 3 and then for days 4 to 6 and compare them.
Starting with 1,200 bacteria and a daily decrease of 10%, the number of bacteria at the end of day 1 is 1,200 × (1 - 0.10) = 1,080. The decrease is 1,200 - 1,080 = 120 bacteria. On day 2, we start with 1,080 bacteria, and it decreases by 10% to 1,080 × (1 - 0.10) = 972. The decrease from day 1 to day 2 is 1,080 - 972 = 108 bacteria. For day 3, the starting number is 972, and after a 10% decrease, it becomes 972 × (1 - 0.10) = 874.8. The decrease on day 3 is 972 - 874.8 ≈ 97.2 bacteria.
Now moving to days 4 to 6, day 4 starts with approximately 874.8 bacteria and decreases by 10%: 874.8 × (1 - 0.10) ≈ 787.3. The decrease is 874.8 - 787.3 ≈ 87.5 bacteria. On day 5, we have about 787.3 bacteria, and after the 10% decrease: 787.3 × (1 - 0.10) ≈ 708.6. The decrease is 787.3 - 708.6 ≈ 78.7 bacteria. Finally, on day 6, starting with approximately 708.6 bacteria and after a 10% decrease: 708.6 × (1 - 0.10) ≈ 637.7. The decrease on day 6 is 708.6 - 637.7 ≈ 70.9 bacteria.
When comparing the total decrease from days 1 to 3 with that from days 4 to 6, we can see that the total decrease from days 1 to 3 is 120 + 108 + 97.2 = 325.2 bacteria, and for days 4 to 6, it is approximately 87.5 + 78.7 + 70.9 = 237.1 bacteria. Consequently, the correct answer is: