Chapter 6.2, Problem 3E

To determine

To compare exponential growth and exponential decay

Answer to Problem 3E

Exponential Growth Function	Exponential Decay Function
The function $f\left(x\right)=a{b}^x,where\text{ a}\ne 0\text{ and }b>1$ is the is said to be exponential growth functions with base b.	The function $f\left(x\right)=a{b}^x,where0<b<1,a\ne 0$ is said to be exponential decay functions with base b.
The graph below shows the general shape of an exponential growth function	The graph below shows the general shape of an exponential growth function
The domain of $f\left(x\right)=b^x$ is all real numbers. The Range is $y>0$	The domain of $f\left(x\right)=b^x$ is all real numbers. The Range is $y>0$

Explanation of Solution

Given information:

Question involving comparison of exponential growth and exponential decay

Comparison between exponential growth and exponential decay is below:

Exponential Growth Function	Exponential Decay Function
The function $f\left(x\right)=b^x,where\text{ a}\ne 0$ is theparent function for the family of exponential growth functions with base b.	The function $f\left(x\right)=b^x,where0<b<1$ is the parent function for the family of exponential decay functions with base b.
The graph below shows the general shape of an exponential growth function	The graph below shows the general shape of an exponential growth function
The domain of $f\left(x\right)=b^x$ is all real numbers. The Range is $y>0$	The domain of $f\left(x\right)=b^x$ is all real numbers. The Range is $y>0$