# How do you graph y=1.1(0.1)^x?

Aug 30, 2015

Note that the graph is exponentially decaying and find some points through which it goes, to find that it is very steep for negative values of $x$ and very flat for positive values.

#### Explanation:

This graph is very steep for negative values of $x$ and very flat for positive values of $x$, passing through the points:

$\left(- 2 , 110\right)$, $\left(- 1 , 11\right)$, $\left(0 , 1.1\right)$, $\left(1 , 0.11\right)$, $\left(2 , 0.01\right)$

graph{1.1*(0.1)^x [-5.23, 4.77, -0.95, 4.05]}

Note that reversing the sign of $x$ or replacing the $0.1$ with $10$ results in the mirror image graph:

graph{1.1*(10)^x [-5.23, 4.77, -0.95, 4.05]}

For practical purposes, it is often more useful to graph the common logarithm of the function instead,

log(y) = log(1.1(0.1)^x)) = log(1.1)+x log(0.1)

$= \log \left(1.1\right) - x \approx 0.04139 - x$

graph{log(1.1(0.1)^x) [-2, 3, -1.12, 1.38]}

Graphing the $\log$ of the function is basically the same as graphing the original function on paper with a logarithmic vertical scale.