Question

Ezra is training for a track race. He starts by sprinting 100 yards. He gradually increases his distance, adding 5 yards a day for 21 days

What explicit formula models this situation?

Answer 1

To create an explicit formula for Ezra's training, we can start by defining a few variables:

- Let \( d \) represent the number of days Ezra has been training.
- The initial distance he sprints on day 0 is 100 yards.
- Each day, he increases the distance by 5 yards.

The distance \( D \) that Ezra sprints on day \( d \) can be modeled as follows:

\[
D(d) = 100 + 5d
\]

where:
- \( D(d) \) is the distance in yards that he sprints on day \( d \),
- 100 is the initial distance in yards,
- 5 is the amount by which he increases the distance each day,
- \( d \) is the number of days (with \( d = 0, 1, 2, \ldots, 21 \)).

So the explicit formula for the distance he sprints on any given day \( d \) is \( D(d) = 100 + 5d \).