Chapter 6.3, Problem 1E

To determine

To describe: the equation and graph of two types of functions that we can use to model data.

Answer to Problem 1E

We can model data by linear function and exponential functions.

Graph of linear function for $ab>1$

Graph of exponential function is,

Explanation of Solution

Given information:

Two types of functions that we can used to model data.

Calculation:

Two equation for data modeling are-

Linear function : The equation is of the form of a straight line $y=mx+c$ . Where $m$ represents the gradient and $c$

1. is the point where the graph crosses the y-axis. Where the first difference are constant.
Graph of $y=mx+c$ is the straight line joining two points $(0,c),\left(-\frac{c}{m},0\right)$ as given in the graph,



Slope of AB= $\frac{c-0}{0-\left(-\frac{c}{m}\right)}=\frac{c}{\frac{c}{m}}=m$ .

Exponential function : The function is of the form $y=a{b}^x$ . While model data by exponential function , a common ration will be there to get the next term. The graph of exponential function $y=a{b}^x$ for $ab>1$ is,