Chapter 11, Problem 25SGA

To determine

Graph the exponential function or inequality.

Answer to Problem 25SGA

  

Explanation of Solution

Given information:

  $y\ge -2^x+1$

Calculation:

Here, we will consider the following:

  $y\ge -2^x+1$

Now, we will find the values of $x$ for different values of $y$ :

  $\begin{array}{ll}x\hfill & y\hfill \\ -5\hfill & -2^{-5}+1=0.96875\hfill \\ -4\hfill & -2^{-4}+1=0.9375\hfill \\ -3\hfill & -2^{-3}+1=0.875\hfill \\ -2\hfill & -2^{-2}+1=0.75\hfill \\ -1\hfill & -2^{-1}+1=0.5\hfill \\ 0\hfill & -2^0+1=0\hfill \\ 1\hfill & -2^1+1=-1\hfill \\ 2\hfill & -2^2+1=-3\hfill \\ 3\hfill & -2^3+1=-7\hfill \\ 4\hfill & -2^4+1=-15\hfill \\ 5\hfill & -2^5+1=-31\hfill \end{array}$

Now, we will plot the points on the graph. Connect the points to graph the function $y\ge -2^x+1$ .

  

Now, we will consider the point $\left(1,1\right)$ and will decide the area of shade:

  $\begin{array}{l}y\ge -2^x+1\\ 1\ge -2^{-1}+1\\ 1\ge -2+1\\ 1\ge -1\\ \therefore True\end{array}$

Hence, the results are shown in the above graph.