On a graph titled Time Spent and Test Grades, a line and ten points are plotted in quadrant 1 of a coordinate plane. The x-axis is labeled Hours Worked, and the y-axis is labeled Grade.

Question

The data in the graph represents the relationship between the amount of time spent studying and test grades. Each point represents a piece of data collected from students who took a test and the grade that student received. For example, (2,70)
represents a student who studied for 2 hours and received a 70. Decide which model best fits this data.

(1 point)
Responses

no model
no model

a linear model
a linear model

a quadratic model
a quadratic model

an exponential model

Answer 1

To determine which model best fits the data representing the relationship between hours worked (studied) and test grades, we need to consider the nature of the relationship.

1. Linear Model: If the points on the graph form a straight line or are roughly clustered around a straight line, this would indicate a linear relationship, suggesting that as studying time increases, grades increase at a constant rate.

2. Quadratic Model: If the data points form a parabola shape (either opening upwards or downwards), a quadratic relationship could be indicated. This would suggest that the relation between studying time and grades involves some acceleration (e.g., after a point, additional study time could lead to diminishing returns in grade improvement).

3. Exponential Model: If the grades increase quickly with small amounts of additional study time and then level off, this suggests an exponential relationship. It typically represents a scenario where initial increases in studying lead to large improvements in grades, but after a certain point, additional study has less effect.

4. No Model: If the points are scattered randomly without any discernible pattern, none of the models would be appropriate.

Without seeing the actual graph, I suggest assessing the visual pattern of the points:

• If they trend upward in a straight line, choose a linear model.
• If they curve upward and then flatten, choose an exponential model.
• If they form a U-shape or inverted U-shape, choose a quadratic model.
• If they appear random, choose no model.

Assuming there is a general consistent trend showing that more study time usually correlates with better grades, a linear model is often a safe assumption. Thus, based on the information you've provided, I would suggest the response is:

a linear model.