Chapter 6.1, Problem 13E

To determine

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

Answer to Problem 13E

The function represents exponential growth

Explanation of Solution

Given information:

The function is $y={\left(\frac{4}{3}\right)}^x$

Step 1 Identify the value of the base. The base is $\frac{4}{3}$ ,is greater than 1, so the function represents exponential growth

Step 2 Make a table of values

$x$	$-2$	$-1$	0	1	2	3
$y$	$\frac{9}{16}$	$\frac{3}{4}$	1	$\frac{4}{3}$	$\frac{16}{9}$	$\frac{27}{64}$

Step 3 plot the point from the table.

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

  

Hence, the function represents exponential growth .