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.

Answer 1

We need x to be nonnegative (can't run negative days) and y ≥ 0 (can't need negative miles). Solve y ≥ 0:

-1.2x + 120 ≥ 0 → x ≤ 100.

So the domain is 0 ≤ x ≤ 100. (If x must be a whole number of days: x ∈ {0, 1, 2, …, 100}.)