Chapter SH, Problem 9.9.9EP

To determine

The graph of $y=5{\left(\frac{2}{5}\right)}^x$ is to be drawn.

Explanation of Solution

Given:

  $y=5{\left(\frac{2}{5}\right)}^x$

Graph:

  

Interpretation:

The given equation is:

  $y=5{\left(\frac{2}{5}\right)}^x$

At $x=2$

  $\begin{array}{l}y=5{\left(\frac{2}{5}\right)}^x\\ y=5{\left(\frac{2}{5}\right)}^2\\ y=0.8\end{array}$

At $x=1$

  $\begin{array}{l}y=5{\left(\frac{2}{5}\right)}^x\\ y=5{\left(\frac{2}{5}\right)}^1\\ y=2\end{array}$

At $x=0$

  $\begin{array}{l}y=5{\left(\frac{2}{5}\right)}^x\\ y=5{\left(\frac{2}{5}\right)}^0\\ y=5\end{array}$

At $x=-2$

  $\begin{array}{l}y=5{\left(\frac{2}{5}\right)}^x\\ y=5{\left(\frac{2}{5}\right)}^{-2}\\ y=31.25\end{array}$

At $x=-1$

  $\begin{array}{l}y=5{\left(\frac{2}{5}\right)}^x\\ y=5{\left(\frac{2}{5}\right)}^{-1}\\ y=12.5\end{array}$

So, the co-ordinates to draw eq. $y=5{\left(\frac{2}{5}\right)}^x$ are

  $\left(2,0.8\right),\left(1,2\right),\left(0,5\right),\left(-2,31.25\right),\left(-1,12.5\right)$