Chapter 4.3, Problem 31E

Solution

The given function $f\left(x\right)=3e^{-x}$ is exponential growth or exponential decay.

The given function $f\left(x\right)=3e^{-x}$ is an exponential decay.

Given information: $f\left(x\right)=3e^{-x}$

Calculation:

The function is,

  $f\left(x\right)=3e^{-x}$

Let $f\left(x\right)$ = $y$

Therefore,

  $y=3e^{-x}$ ......(1)

A function $y$ = $a{b}^x$ is exponential decay when $b$ falls between 0 and 1. The value of $a$ can never be zero and the value of b can never be one.

A function $y$ = $a{b}^x$ is exponential growth when $b$ is greater than one. The value of $a$ can never be zero.

Now put the values like 0,1, 2, 3......in (1)

Note that as $x$ become larger the value of $e^{-x}$ approaches zero.so, this is a exponential decay function.

Column1	Column2	Column3	Column4	Column5	Column6
x	0	1	2	3	4
y	3	1.1036	0.406	0.14936	0.05494

  

From the graph it can be seen as the values decrease every time.

Therefore, the given function is an exponential decay function.