Question

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

Answer 1

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:

`(-2, 110)`, `(-1, 11)`, `(0, 1.1)`, `(1, 0.11)`, `(2, 0.01)`

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(1.1)-x ~~ 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.