Final answer:
The school will close after 10 days because that's when the number of infected students reaches 600.
Step-by-step explanation:
To determine the number of days it will take for the school to close, we need to calculate the number of students infected each day. If 600 of the 700 students need to be infected for the school to close, that means there will be 100 healthy students remaining. Let's assume that the number of infected students doubles each day.
- On day 1: 1 student is infected
- On day 2: 2 students are infected
- On day 3: 4 students are infected
- On day 4: 8 students are infected
- On day 5: 16 students are infected
- On day 6: 32 students are infected
- On day 7: 64 students are infected
- On day 8: 128 students are infected
- On day 9: 256 students are infected
- On day 10: 512 students are infected
Therefore, the school will close after 10 days (option c) because on that day, the number of infected students reaches 600.