Chapter 6.1, Problem 50E

(a)

To determine

To Show: $\frac{f(x+1)}{f(x)}=b$ .

Explanation of Solution

Given: $f(x)=a{b}^x$

Given: $f(x)=a{b}^x$

Now

  $\begin{array}{l}f(x+1)=a{b}^{x+1}\\ now\\ \frac{f(x+1)}{f(x)}=\frac{a{b}^{x}b}{a{b}^x}=b\end{array}$

Hence proved.

(b)

To determine

To Explain: Why there is no exponential solution of the form $f(x)=a{b}^x$ using the given table.

Answer to Problem 50E

  $\begin{array}{l}\frac{f(1)}{f(0)}=1\\ \frac{f(2)}{f(1)}=2\\ \frac{f(3)}{f(2)}=3\\ \frac{f(4)}{f(3)}=3\end{array}$

Explanation of Solution

Given:

  

Using $f(x)=a{b}^x$

  $\begin{array}{l}\frac{f(1)}{f(0)}=1\\ \frac{f(2)}{f(1)}=2\\ \frac{f(3)}{f(2)}=3\\ \frac{f(4)}{f(3)}=3\end{array}$