Chapter 6.1, Problem 11E

To determine

To tell: whetherthe function represent exponential growth or exponential decay.

Answer to Problem 11E

The function represents exponential decay

Explanation of Solution

Given information :

The function is $y={\left(\frac{1}{6}\right)}^x$

Step 1Identify the value of the base. The base is $\frac{1}{6}$ ,is greater than 0, and smaller than 1,so the function represents exponential decay

Step 2 Make a table of values

$x$	$-2$	$-1$	0	1	2	3
$y$	$36$	$6$	1	$\frac{1}{6}$	$\frac{1}{36}$	$\frac{1}{216}$

Step 3 plot the point from the table.

Step 4 Draw from right to left, a smooth curve that begin just above the $x$ -axis, passes through the plotted points, and moves up to the left.

  

Hence, the function represents exponential decay.