Chapter 8.6, Problem 14E

To determine

To plot: The points $\left(0,8\right),\left(-4,0.25\right),\left(-3,0.4\right),\left(-2,1\right),\left(-1,3\right)$ on the graph and identify the representation of the points.

Answer to Problem 14E

Thepoints $\left(0,8\right),\left(-4,0.25\right),\left(-3,0.4\right),\left(-2,1\right),\left(-1,3\right)$ represent theexponential equation.

Explanation of Solution

Given information:

The points are $\left(0,8\right),\left(-4,0.25\right),\left(-3,0.4\right),\left(-2,1\right),\left(-1,3\right)$ .

Plot the points on the graph as shown in Figure 1.

  

The exponential function is monotonic, defined on the set of real numbers.

The equation of the exponential function is $e^{ax}$ where the value of $a$ determines the graph is decreases or increases and always passes through the $y$ axis such that the graph is asymptotic to the $x$ axis.

The exponential function approaches infinity when the value of $a$ is positive or function approaches 0 when the value of $a$ is negative.

It can be seen from the given graph that the function is monotonically increasing, defined on the set of real numbers and will pass through the $y$ axis if the curve gets extend.

The function approaches 0 since the function is increasing such that the graph is asymptotic to the $x$ axis.

Therefore, the points on the graph represents the equation of exponential function.