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Let an exponential function take the form
$$y=a \cdot b^x$$ I know if a is greater than $0$ and b is greater than $1$, this is called exponential growth.

What if a is less than $0$ and b is greater than $1$? Is this still exponential growth?

Salinas
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  • Yes it is, in the sense that the absolute value is growing. – Lubin Jan 12 '19 at 04:07
  • I’ve heard it being called exponential decay in the sense that the value decreases, but it might also be referred to as negative exponential growth in the sense the values become more negative (increasing absolute value). Names aren’t often assigned to the $a < 0$ case though. – KM101 Jan 12 '19 at 04:11

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When $b<1$, this is known as “exponential decay” and is a common term as it is used to model many systems. The case $a<0$ is less commonly used and doesn’t have a generally agreed upon name, I’ve heard it called exponentially decreasing though.

Tyler6
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