Question
or Deb wants to join her school's track team this year, so she has been running laps every day to train. She averages 2 minutes per lap, and now she's curious how much time she has spent running in total. You can use a function to approximate the total number of minutes Deb spent running x laps. Is the function linear or exponential? Which equation represents the function?
Answers
GPT-4o mini
The function that approximates the total number of minutes Deb has spent running \( x \) laps is linear. This is because the time spent running increases proportionally with the number of laps.
To represent the time spent running, we can use the equation:
\[
T(x) = 2x
\]
Where:
- \( T(x) \) is the total time in minutes,
- \( x \) is the number of laps,
- The coefficient \( 2 \) represents the average time (in minutes) that Deb takes to run each lap.
Since the function \( T(x) = 2x \) has a constant rate of change (i.e., for every additional lap, Deb spends an additional 2 minutes), it is a linear function.
To represent the time spent running, we can use the equation:
\[
T(x) = 2x
\]
Where:
- \( T(x) \) is the total time in minutes,
- \( x \) is the number of laps,
- The coefficient \( 2 \) represents the average time (in minutes) that Deb takes to run each lap.
Since the function \( T(x) = 2x \) has a constant rate of change (i.e., for every additional lap, Deb spends an additional 2 minutes), it is a linear function.