Chapter 6, Problem 12CR

To determine

To find: whether the table of values represents a linear or an exponential function and then writes the function.

Answer to Problem 12CR

Exponential function.

  $y=96{(0.25)}^x.$

Explanation of Solution

Given information: Given table values is shown in the below table.

x	-1	0	1	2	3
y	384	96	24	6	1.5

Calculation:

From the given table values when x increases by 1, y is multiplied by the constant factor $\frac{1}{4}$ , therefore the function is exponential.

Therefore, the function is in the form of $y=a{b}^x$ .

From the table values:

  $\begin{array}{l}a{b}^0=96\Rightarrow a=96\\ a{b}^1=24\Rightarrow b=\frac{24}{a}\Rightarrow b=\frac{24}{96}\Rightarrow b=\frac{1}{4}=0.25\\ $ y=96{(0.25)}^x.$\end{array}$