Chapter 7.7, Problem 10PPS

To determine

The exponential function by using the points on the given graph.

Answer to Problem 10PPS

The exponential function is $y=3^x$ .

Explanation of Solution

Given information:In the given graph, two points given, $(1,3)$ and $(0,1)$ .

Calculation:

Let, the exponential function be $y=a{b}^x$ .

It contains the given points $(1,3)$ and $(0,1)$ .

By taking the point $(0,1)$ , the values we plug in are x=0 and y=1,

  $\begin{array}{l}y=a{b}^x\\ \Rightarrow 1=a{b}^0\\ \Rightarrow 1=a(1)\\ \Rightarrow 1=a\\ \therefore a=1\end{array}$

Now by taking the point $(1,3)$ , the values we plug in are x=1,y=3,

  $\begin{array}{l}y=a{b}^x\\ \Rightarrow 3=a{b}^1\\ \Rightarrow 3=ab\\ \Rightarrow 3=(1)b\\ \Rightarrow 3=b\\ \therefore b=3\end{array}$

So, the exponential function is

  $\begin{array}{l}$ y=1{(3)}^x$\Rightarrow y=3^x\end{array}$

  $\therefore$ The exponential function is $y=3^x$ .