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 (c) Which is more appropriate for modeling this data: an exponential function or a power function?

Answer 1

The appropriateness of an exponential model versus a power model depends on the growth pattern exhibited by the data. Exponential growth is consistent percentage increase, while power growth is related to a function where the y-value is a power of x. Without graphing or applying statistical modeling, it is difficult to conclusively determine the best fit for the provided data points.

Step-by-step explanation:

In determining whether an exponential function or a power function is more appropriate for modeling the given data, we should look for patterns that the functions typically represent. An exponential model is characterized by a consistent percentage growth rate, resulting in a J-curve when graphed. This means that as the x-value increases, the rate of increase in the y-value accelerates at a consistent percent rate. In contrast, a power function exhibit a growth pattern where the y-value increases as a power of x, typically described by a polynomial equation like y = axb, where 'a' and 'b' are constants.

To determine which model fits the given data points better, we could plot these points on a graph and visually assess the trend, or conduct a statistical test like linear regression on the logarithm of the given y-values versus the x-values for the exponential model, or on the log-log plot for the power mode.