Chapter 6.1, Problem 19E

To determine

To find: The value of $b$

Answer to Problem 19E

  $b=3$

Explanation of Solution

Given information: $f\left(x\right)=b^x$

  

Concept used:

$x$$0$$1$$2$$3$$y$$a_0$$a_1$$a_2$$a_3$

If the consecutive ratio of the y-values are all equal to a common value r, then y can be modeled by an exponential function.

  $\begin{array}{l}r=\frac{a_n+1}{a_n}\text{ common ratio}\\ y=a_0{r}^x\end{array}$

Calculation:

$x$$-1$$0$$1$$f\left(x\right)$$\frac{1}{3}$$1$$3$

  $f\left(x\right)=b^x=1\times b^x$

If is an exponential function.

We can think $b$ as common ratio.

So, $b=\frac{3}{1}=3$

  $\therefore b=3$

Therefore, $b=3$