Question

Exponential or Power Model? Data points (x, y) are shown in the table. x 2 4 6 8 10 12 14 16 y 0.08 0.12 0.18 0.25 0.36 0.52 0.73 1.06 (d) Find an appropriate function to model the data.

Answer 1

To model the given data, a power model would be more appropriate than an exponential model. The y-values increase at a varying rate, indicating the need for a power function.

Step-by-step explanation:

To determine whether an exponential or power model is appropriate for the given data, we can examine the pattern of the y-values. If the y-values increase or decrease at a constant rate, an exponential model is suitable. If the y-values increase or decrease at a varying rate, a power model is more appropriate.

In this case, let's examine the y-values: 0.08, 0.12, 0.18, 0.25, 0.36, 0.52, 0.73, 1.06. Notice that the rate at which the y-values increase is not constant. For example, the increase from 0.08 to 0.12 is 0.04, but the increase from 0.73 to 1.06 is 0.33. This indicates that a power model would be a better fit for the data.

A power model can be represented by a function of the form y = ax^b, where a and b are constants. We can use regression analysis to determine the values of a and b that best fit the data.