Chapter 6.3, Problem 2E

To determine

To decide: whether to use a linear or an exponential function to model a data set.

Answer to Problem 2E

By observing constant difference for linear model and constant ratio for the exponential data model.

Explanation of Solution

Calculation:

In case of using of linear equation $y=mx+c$ , the difference of each term of the sequence of values remain constant. For example for a data set $(x,f(x))=\{(0,-6),(1,-1),(2,4),(3,9),\mathrm{.......}\}$ the values $-6,-1,4,9,\mathrm{....}$ are in a constant difference of $5$ .

In case of exponential data modeling there must be a common ratio between each term of the given data. For example for the data set $(x,f(x))=\{(0,50),(1,20),(2,8),(3,3.2),\mathrm{.......}\}$ ,

  $\begin{array}{l}\frac{20}{50}=\frac{2}{5}\\ \frac{8}{20}=\frac{2}{5}\\ \frac{3.2}{8}=\frac{2}{5}\mathrm{......}\end{array}$

Thus there is a common ratio multiplication of $0.4$ to get the next term.