Final answer:
To fit a curve to the data points, Riley should create a scatter plot, analyze the data distribution, use a calculator's regression function to find the best fitting equation, add this regression line or curve to the plot, and check the correlation coefficient for its significance.
Step-by-step explanation:
The question pertains to the process of fitting a curve to a set of data points using various types of functions. The student has already attempted to use a cubic function and needs to decide among a linear, quadratic, cubic, or exponential model based on the appearance of the data on a coordinate grid. Here is how to approach this problem:
Enter the collected data into a calculator to create a scatter plot. This graphical representation will display all the data points in a two-dimensional plane.
Analyze the scatter plot to deduce the nature of the relationship between the variables. If the data points are aligned in a straight line, a linear function is most suitable. If the data takes the shape of a parabola, a quadratic function should be used. For an S-shaped curve, a cubic function is appropriate, and for rapid increase or decrease, an exponential function could fit.
Use the calculator's regression function to determine the best fit line or curve. For a linear fit, the equation will be in the form y = a + bx, where a is the y-intercept, and b is the slope. For the other types of functions, the equation will differ based on the degree and characteristics of the curve.
Once the regression equation is obtained, overlay this regression line or curve onto your scatter plot.
Examine the correlation coefficient to assess the strength of the relationship. A significant correlation coefficient suggests a strong linear relationship between the variables.
In summary, the student should use the regression function to find an equation that best fits the data, whether it be a linear, quadratic, cubic, or exponential model, based on the shape of the data points' distribution.