Exponential Growth and Decay

When a > 0 and the b is greater than 1, the graph will be increasing (growing).

For this example, each time x is increased by 1, y increases by a factor of 2.

      This would be considered exponential growth.

When a > 0 and the b is between 0 and 1, the graph will be decreasing (decaying).

For this example, each time x is increased by 1, y decreases to one half of its previous value.

      This would be considered exponential decay.

Exponential growth and decay are mathematical changes. The rate of the change continues to either increase or decrease as time passes. In exponential growth, the rate of change increases over time - the rate of the growth becomes faster as time passes. In exponential decay, the rate of change decreases over time - the rate of the decay becomes slower as time passes.

Major Note: Since the rate of change is not constant (the same) across the entire graph, these functions are not straight lines.

#Calculus #ExponentialGrowth #Decay #Growth #ExponentialDecay

Easy Math Editor

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`bold` or `__bold__`	bold
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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$