To determine whether the situation represents a linear or non-linear function, we need to inspect the relationship between the elapsed time in minutes and the number of math problems completed.
Let's analyze the data you've provided:
- At 1 minute, Jana completed 3 problems.
- At 2 minutes, she completed 7 problems.
- At 3 minutes, she completed 12 problems.
- At 4 minutes, she completed 16 problems.
- At 5 minutes, she completed 19 problems.
Now, let's examine the change in the number of problems completed as the minutes increase:
- From 1 minute (3 problems) to 2 minutes (7 problems): increase of 4 problems.
- From 2 minutes (7 problems) to 3 minutes (12 problems): increase of 5 problems.
- From 3 minutes (12 problems) to 4 minutes (16 problems): increase of 4 problems.
- From 4 minutes (16 problems) to 5 minutes (19 problems): increase of 3 problems.
The increments between the number of problems completed are not consistent:
- Between 1 and 2 minutes: +4
- Between 2 and 3 minutes: +5
- Between 3 and 4 minutes: +4
- Between 4 and 5 minutes: +3
Since the differences in the number of problems completed are not constant, this means that the function does not produce a straight line when graphed on a coordinate system.
Therefore, this situation represents a non-linear function because the number of math problems completed per minute does not have a constant rate of change.
In a linear function, you would expect the same amount of increase (constant slope) in the number of math problems completed for every minute, which is not the case here.