Chapter 4.3, Problem 37E

Solution

The given function $f\left(x\right)=2e^{4x}$ is exponential growth or exponential growth.

The given function $f\left(x\right)=2e^{4x}$ is an exponential growth.

Given information: $f\left(x\right)=2e^{4x}$

Calculation:

The function is,

  $f\left(x\right)=2e^{4x}$

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

Therefore,

  $f\left(x\right)=2e^{4x}$ ......(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)

Column1	Column2	Column3
x	0	1
y	2	109.19

  

Note that as $x$ become larger the value of $e^{4x}$ grows without bound. So, this is an exponential growth function.

We get that the values increase every time.

Therefore, the given function is an exponential growth function.