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 representing Lowell's daily runs, we need to analyze the constraints based on his running goal and daily distance.

1. Understanding the goal: Lowell aims to run a total of 120 miles.
2. Daily distance: He runs 1.2 miles per day.

To find out how many days he will run before reaching his goal:

• Total miles = 120 miles
• Daily miles = 1.2 miles

The number of days he will run can be calculated as: \[ \frac{120 \text{ miles}}{1.2 \text{ miles/day}} = 100 \text{ days} \]

This means Lowell will run for a maximum of 100 days. The minimum number of days is 0 (he has not started running yet).

Thus, the domain in terms of \(x\) (the number of days he runs) can be expressed as: \[ 0 \leq x \leq 100 \]

So the inequality that represents the domain is: \[ 0 \leq x \leq 100 \]