Chapter 7, Problem 15CT

To determine

To find: the function $\frac{1}{2}\cdot 4^x$ .

Answer to Problem 15CT

The value of functions at -1, 2 and 3 are $\frac{1}{8}$ , $8$ and $32$ respectively.

Explanation of Solution

Given:

The function is $\frac{1}{2}\cdot 4^x$ . The values of x are -1, 2 and 3.

Calculation:

The value of function at x = -1 is calculated as follows:

  $\begin{array}{c}f\left(-1\right)=\frac{1}{2}\cdot 4^{\left(-1\right)}\\ =\frac{1}{2}\cdot \frac{1}{4}\\ =\frac{1}{8}\end{array}$

The value of function at 2 is calculated as follows:

  $\begin{array}{c}f\left(2\right)=\frac{1}{2}\cdot 4^{\left(2\right)}\\ =\frac{1}{2}\cdot 16\\ =8\end{array}$

The value of function at 3 is calculated as follows:

  $\begin{array}{c}f\left(3\right)=\frac{1}{2}\cdot 4^{\left(3\right)}\\ =\frac{1}{2}\cdot 64\\ =32\end{array}$

Thus, the value of functions at -1, 2 and 3 are $\frac{1}{8}$ , $8$ and $32$ respectively.