The Natural Base e

We are asked to state the type of function and then draw a graph. Let's do these things one at a time.

Type of Function

To determine whether the given function represents exponential growth or exponential decay, let's recall two properties of the natural base exponential function, $y = a e^{r x} .$

$y = a e^{r x}$
$a > 0$ and $r > 0$	$a > 0$ and $r < 0$
Exponential growth function	Exponential decay function

Let's now consider the given function. $y = 3 e^{2 x}$ Since both $a = 3$ and $r = 2$ are greater than zero, the function is an exponential growth function.

Graph

Next, let's make a table of values to graph the function.

$x$	$3 e^{2 x}$	$y = 3 e^{2 x}$
$- 1$	$3 e^{2 (- 1)}$	$\approx 0.4$
$0$	$3 e^{2 (0)}$	$3$
$\frac{1}{2}$	$3 e^{2 (\frac{1}{2})}$	$\approx 8.15$
$1$	$3 e^{2 (1)}$	$\approx 22.12$

Finally, we will plot the points and connect them with a smooth curve.

The Natural Base e 1.6 - Solution

Type of Function

Graph