Chapter 6, Problem 1CR

To determine

To tell: whether the function represent exponential growth or exponential decay.

Answer to Problem 1CR

The function represents exponential decay

Explanation of Solution

Given information:

The function is $y={\frac{1}{3}}^x$

Step 1 Identify the value of the base. The base, $\frac{1}{3}$ 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
$y$	$9$	$3$	1	$\frac{1}{3}$	$\frac{1}{9}$

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.