Question

sean began jogging to live a healthier lifestyle. on his first run, he ran one - half mile. he increased his workouts by adding two miles a month to his run. he wrote the equation $f(x)=0.5 + 2x$ to model his progress. the variable $x$ represents the number of
○ miles he runs.
○ months he runs.
○ miles he ran the first day.
○ calories he burns.

Explanation:

To determine what \( x \) represents, we analyze the context and the equation \( f(x)=0.5 + 2x \). The initial distance (first run) is \( 0.5 \) miles. He adds \( 2 \) miles per month. So the term \( 2x \) should represent the total additional miles over \( x \) months. Thus, \( x \) must represent the number of months he runs. Let's check the other options:

• "miles he runs" would not make sense as \( 2x \) would be inconsistent (he adds 2 miles per month, not per mile run).
• "miles he ran the first day" is \( 0.5 \), not \( x \).
• "calories he burns" is not related to the distance - based model here.

Answer:

B. months he runs.