Question

The table shows the growth y (in inches) of an elk's antlers during week x. The equation y = - 0.7 + 6.8 models the data. Is the model a good fit? Explain.

Answer 1

The model is not a good fit because it doesn’t sync up completely with the equation listed. Since y=-0.7x+6.8 (where y is the growth and x is the number of weeks) is the equation to graph, the table is not completely accurate because…

If you were to substitute x for the number of weeks, in this case, I’ll do one week, the equation would be -0.7 + 6.8. This comes out to 6.1 inches. In the graph it shows that the same problem comes out to 6.0 inches. Therefore, this is not a good graph to illustrate the equation given. Hope this helps!

Answer 2

The model y = -0.7x + 6.8 is a good fit for the data as the predicted values closely match the actual values.

The equation y = -0.7x + 6.8 models the growth of an elk's antlers during different weeks. To determine if the model is a good fit, we can compare the predicted values from the model to the actual values given in the table. Let's calculate the predicted values and compare them to the actual values:

For x = 1, the predicted y value is -0.7(1) + 6.8 = 6.1

For x = 2, the predicted y value is -0.7(2) + 6.8 = 5.4

For x = 3, the predicted y value is -0.7(3) + 6.8 = 4.7

For x = 4, the predicted y value is -0.7(4) + 6.8 = 4.0

For x = 5, the predicted y value is -0.7(5) + 6.8 = 3.3

We can see that the predicted values closely match the actual values given in the table. Therefore, the model y = -0.7x + 6.8 is a good fit for the data.