To solve the question of what the variable [tex]\( x \)[/tex] represents in the equation [tex]\( f(x) = 0.5 + 2x \)[/tex], let's carefully analyze the context and the equation itself:
1. Understanding the Context: Sean started jogging and ran [tex]\( 0.5 \)[/tex] miles on his first day. He is increasing his running distance by [tex]\( 2 \)[/tex] miles every month.
2. Analyzing the Equation: The equation [tex]\( f(x) = 0.5 + 2x \)[/tex] represents his progress over time. Here’s a detailed breakdown:
- [tex]\( f(x) \)[/tex] is the total distance he runs after [tex]\( x \)[/tex] months.
- The constant term [tex]\( 0.5 \)[/tex] represents the initial distance he ran on the first day.
- The term [tex]\( 2x \)[/tex] signifies the increase in his running distance over time, where he adds [tex]\( 2 \)[/tex] miles each month.
3. Interpreting the Variable [tex]\( x \)[/tex]: From the equation [tex]\( f(x) = 0.5 + 2x \)[/tex]:
- [tex]\( x \)[/tex] must represent the number of months he has been increasing his running distance, since the increase is in miles added per month.
4. Conclusion:
- The given options were:
1. Number of miles he runs
2. Months he runs
3. Miles he ran the first day
4. Calories he burns
- Based on the context and the structure of the equation, [tex]\( x \)[/tex] clearly represents the number of months he runs since it indicates the period over which he is increasing his running.
Therefore, the variable [tex]\( x \)[/tex] represents the number of months he runs.
