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

Question

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:

\[ 0 \leq x \leq 100 \]