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≤
.

Answer 1

To determine the domain of the function \(y = -1.2x + 120\) in the context of the problem, we need to consider the number of days \(x\) that Lowell can run based on his goal of reaching 120 miles.

1. **Finding the maximum number of days:** Since Lowell runs 1.2 miles daily and wants to complete a total of 120 miles, we can calculate how many days he needs to run:

\[
\text{Number of days (x)} = \frac{\text{Total miles goal}}{\text{Miles per day}} = \frac{120}{1.2} = 100
\]

Therefore, he will run for a maximum of 100 days.

2. **Finding the minimum number of days:** The minimum number of days he can run is 0 days (he hasn't started running yet).

Putting this together, the domain of the function \(y\) in terms of the number of days \(x\) is:

\[
0 \leq x \leq 100
\]

Thus, the domain can be represented by the inequality:

\[
0 \leq x \leq 100
\]