Chapter 7.7, Problem 1CYU

To determine

To construct an exponential function to model the given graph.

Answer to Problem 1CYU

  $y=0.5{\left(3\right)}^x$

Explanation of Solution

Given:

  

Calculation:

Given curve passes through the points $\left(0,0.5\right)\&\left(2,4.5\right)$ .

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 $\left(2,4.5\right)$ in $y=a\cdot b^x$ , we get

  $\begin{array}{l}4.5=a\cdot b^2\\ \Rightarrow 0.5b^2=4.5\\ \Rightarrow b^2=9\\ \Rightarrow b=3\end{array}$

Hence the required exponential function is,

  $y=0.5{\left(3\right)}^x$