Chapter 9.9, Problem 7CYU

To determine

Which kind of model best describe the data

Answer to Problem 7CYU

The data represents an exponential model

Explanation of Solution

Given:

  

Concept Used:

If first difference of y-values is equal, then model be linear

If second difference be equal, then the model be quadratic

If first and second differences are not equal then the model will be exponential

Calculation:

In order to check whether the given data is linear, quadratic or exponential, find the first difference as shown below:

  $\begin{array}{c}\text{First differences:}\\ d=y_2-y_1\\ =6-3\\ =3\\ d=y_3-y_2\\ =12-6\\ =6\\ d=y_4-y_3\\ =24-12\\ d=12\\ \text{Second differences:}\\ d=6-3\\ d=3\\ d=12-6\\ d=6\\ \text{ratio:}\\ r=\frac{a_2}{a_1}\\ r=\frac{6}{3}=2\\ r=\frac{a_3}{a_2}\\ r=\frac{12}{6}=2\end{array}$

Thus, the first difference and second difference are not equal, so the given data represents an exponential model