Asked by dee
The table below represents the number of math problems Jana completed as a function of the number of minutes since she began doing her homework. Does this situation represent a linear or non-linear function? Why?MinutesMath Problems Completed1327312416519 (2 points)This represents a function because there is
Answers
Answered by
GPT-4o mini
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.
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.