Chapter 7.7, Problem 13PPS

To determine

To construct an exponential function to model the given graph.

Answer to Problem 13PPS

  $y=-0.5{\left(4\right)}^x$

Explanation of Solution

Given:

  

Calculation:

Given curve passes through the points $\left(0,-0.5\right)\&\left(1,-2\right)$ .

Let the required exponential function be

  $y=a\cdot b^x$

Now put $\left(0,-0.5\right)$ in $y=a\cdot b^x$ , we get

  $\begin{array}{l}-0.5=a\cdot b^0\\ \Rightarrow a\cdot 1=-0.5\\ \Rightarrow a=-0.5\end{array}$

Now put $\left(1,-2\right)$ in $y=a\cdot b^x$ , we get

  $\begin{array}{l}-2=a\cdot b^1\\ \Rightarrow -0.5b=-2\\ \Rightarrow b=4\end{array}$

Hence the required exponential function is,

  $y=-0.5{\left(4\right)}^x$