Final answer:
To find the expected attendance on the seventh day of the Sunny Day Festival, we calculate the daily increase rate based on the first and third days and apply it to the equation for linear growth, resulting in an expected attendance of 496 people on the seventh day.
Step-by-step explanation:
To determine how many people will attend the Sunny Day Festival on the seventh day, assuming the attendance increases linearly, we first need to calculate the daily increase rate using the information given for the first and third days. The attendance on the first day was 325 people, and it increased to 382 people by the third day. To find the daily increase, we subtract the first day's attendance from the third day's attendance and then divide by the number of days in between:
Daily Increase = (Attendance on Day 3 - Attendance on Day 1) / (Day 3 - Day 1)
Daily Increase = (382 - 325) / (3 - 1) = 57 / 2 = 28.5 people per day
Now that we know the attendance is increasing by 28.5 each day, we can calculate the expected attendance on the seventh day:
Expected Attendance on Day 7 = Attendance on Day 1 + (Daily Increase × (Day 7 - Day 1))
Expected Attendance on Day 7 = 325 + (28.5 × (7 - 1))
Expected Attendance on Day 7 = 325 + (28.5 × 6)
Expected Attendance on Day 7 = 325 + 171 = 496 people
Therefore, we expect that 496 people will attend the festival on the seventh day.