Question

Lowell runs 1.2 miles daily. His goal is to run 120 miles, and he will end his daily runs when he reaches that goal. He uses the equation y=−1.2x+120
to keep track of the distance he still needs to run over time. In this function, x represents the number of days he runs, and y represents the number of miles he must still run to achieve his goal. Complete the inequality to determine the domain of the function given the real-world constraints of the problem.(1 point)
The domain can be represented by the inequality
≤x≤
.
Remaining Attempts : 3
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Answer 1

To determine the domain of the function \( y = -1.2x + 120 \) given the real-world constraints of Lowell's running situation, we need to consider how \( x \) (the number of days he runs) can vary:

1. **Minimum \( x \)**: Lowell starts running on day 0, so \( x \) must be at least 0. Therefore, the lower bound of the domain is \( x \geq 0 \).

2. **Maximum \( x \)**: Lowell runs a total of 120 miles at a rate of 1.2 miles per day. To find the maximum number of days he can run before reaching his goal, we set up the equation:
\[
1.2x = 120
\]
Solving for \( x \), we get:
\[
x = \frac{120}{1.2} = 100
\]

Thus, \( x \) cannot exceed 100 days.

Combining both pieces of information, the domain can be expressed as:
\[
0 \leq x \leq 100
\]

So, the completed inequality representing the domain is:
\[
0 \leq x \leq 100
\]