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

Answer 1

To determine the domain of the function \( y = -1.2x + 120 \), we need to consider the real-world constraints of Lowell's running scenario.

1. **Initial condition**: On day 0, Lowell has not run at all, so \( x = 0 \).
2. **Goal**: Lowell's goal is to run a total of 120 miles. Since he runs 1.2 miles each day, to determine how many days it will take him to reach this goal, we can set up the equation:

\[
1.2x = 120
\]

Solving for \( x \):

\[
x = \frac{120}{1.2} = 100
\]

Therefore, he will reach his goal in 100 days.

Based on these considerations:
- The lower limit for \( x \) is 0 (he hasn't started running yet).
- The upper limit for \( x \) is 100 (the day he completes his 120 miles).

Thus, the domain can be represented by the inequality:

\[
0 \leq x \leq 100
\]

In interval notation, this would be [0, 100].