# How do you determine if the equation y=10(1.1)^x  represents exponential growth or decay?

Apr 25, 2016

#### Explanation:

$y = 10 {\left(1.1\right)}^{x} = 10 {e}^{x \ln 1.1}$

$y ' = \left(10 \ln 1.1\right) {e}^{x \ln 1.1} = \left(10 \ln 1.1\right) {\left(1.1\right)}^{x} = 0.9531 {\left(1.1\right)}^{x} > 0.$

So, y is an exponentially increasing function

Note that, ${\left(1.1\right)}^{x} = {e}^{x \ln 1.1} > 0$, for any x...
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