Final answer:
A recursive formula for the number of minutes Tₙ that Isabel swims on the n th day of her program can be obtained by adding 1/2 minute to the number of minutes she swims on the previous day.
Step-by-step explanation:
A recursive formula for the number of minutes Tₙ that Isabel swims on the n th day of her program can be obtained based on the given information. We know that Isabel swims 10 to 20 laps in a 50-meter pool every day, and she tracks the time it takes her to complete the laps in minutes. Let Tₙ represent the number of minutes she swims on the n th day.
From the given information, we can observe that the number of minutes she swims on each day is 1/2 minute more than the previous day.
Therefore, the recursive formula for the number of minutes Tₙ can be written as:
Tₙ = Tₙ₋₁ + 1/2
Where Tₙ₋₁ represents the number of minutes she swims on the (n-1) th day.