Chapter 7.7, Problem 9PPS

To determine

To construct: the exponential model to the given graph.

Answer to Problem 9PPS

The exponential model of given graph is $y=\left(\frac{1}{4}\right)2^x.$

Explanation of Solution

Given information:

Consider the inequality

  

Calculation:

The given graph is exponentially increasing and it is passing through the points

  $(2,1),(4,4)$ .

The exponential model ist

  $\begin{array}{l}y=a{b}^x\\ (2,1)\Rightarrow 1=a{b}^2\mathrm{.....}(1)\\ (4,4)\Rightarrow 4=a{b}^4\mathrm{....}(2)\\ \frac{(2)}{(1)}\Rightarrow \frac{a{b}^4}{a{b}^2}=\frac{4}{1}\\ b^2=4\\ b=2\\ \Rightarrow a=1/4\end{array}$

Then, $y=\left(\frac{1}{4}\right)2^x$

Hence, the exponential model $y=\left(\frac{1}{4}\right)2^x.$