Final answer:
To find the population on Week 26 of a bug population showing a geometric sequence, calculate the common ratio and apply it to the population on Week 1.
Step-by-step explanation:
The growth of the bug population shows a geometric sequence where the number of bugs increases or decreases by a constant ratio each week. To find the population on Week 26, we need to find the common ratio of the sequence and apply it to the population on Week 1.
- Calculate the common ratio by dividing the population on Week 2 by the population on Week 1: 600 / 500 = 1.2
- Apply the common ratio to the population on Week 1 to find the population on Week 26: 500 * (1.2)^(26-1) = 47,697.9
Therefore, the population on Week 26 is approximately 47,698 bugs.