Chapter 8.3, Problem 55E

To determine

To compare: The graph of $a_n=5{\left(3\right)}^{n-1}$ where $n$ is a positive integer, to the graph of $f(x)=5\cdot 3^{x-1}$ where $x$ is a real number.

Explanation of Solution

Given information:

There are two geometric sequence first $a_n=5{\left(3\right)}^{n-1}$ where $n$ is a positive integer, to the graph of $f(x)=5\cdot 3^{x-1}$ where $x$ is a real number.

Calculation:

There are two geometric sequence first $a_n=5{\left(3\right)}^{n-1}$ where $n$ is a positive integer, to the graph of $f(x)=5\cdot 3^{x-1}$ where $x$ is a real number.

Plotting graph of $a_n=5{\left(3\right)}^{n-1}$ , where $n$ is a positive integer using a graphing utility.

Similarly, plotting graph of $f(x)=5\cdot 3^{x-1}$ where $x$ is a real number using a graphing utility as below.

From above two graph it is observed that both graphs are similar, only difference is graph for $f(x)=5\cdot 3^{x-1}$ is continuous while graph for $a_n=5{\left(3\right)}^{n-1}$ is only positive discrete values of $n$ .