Question

The first time Mya competed in a 500 meter free style race, her time was 15 minutes flat. Each subsequent race, Mya's time was reduced by 10 seconds.

Complete the statement.

(2 points)
The context is best represented by
and the domain is

Answer 1

Is the context linear or a arithmetic sequence and is the domain discrete or continuous

Answer 2

The context is best represented by the equation \( T(n) = 15 \text{ minutes} - (10 \text{ seconds} \times n) \), where \( T(n) \) is Mya's time in minutes for her \( n \)-th race.

The domain is \( n \geq 0 \), where \( n \) represents the number of races Mya has completed (starting with 0 for her first race).

To convert the time into a more consistent unit, you might also express her time in seconds, which would be:

\( T(n) = 900 \text{ seconds} - 10n \), where \( n \geq 0 \).

So,

The context is best represented by \( T(n) = 900 - 10n \) seconds, and the domain is \( n \geq 0 \).

Answer 3

In the context of Mya's race times:

1. **Is the context linear or an arithmetic sequence?**
- The context can be described as both linear and as an arithmetic sequence.
- It is **linear** because the relationship between the number of races \( n \) and Mya's time \( T(n) \) can be represented by a linear equation of the form \( T(n) = 900 - 10n \). This means the time decreases at a constant rate with each race.
- It is also an **arithmetic sequence** since the times form a sequence where each term is obtained by subtracting a fixed amount (10 seconds) from the previous term. The first term is 900 seconds (15 minutes) and subsequent terms are 890 seconds, 880 seconds, and so on.

2. **Is the domain discrete or continuous?**
- The domain is **discrete** because \( n \), the number of races, can only take on whole number values (0, 1, 2, ...). Mya can only complete a whole number of races; hence her times are defined only at these specific points.

In summary:
- The context is both linear and an arithmetic sequence.
- The domain is discrete.