Question 1090792
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a) Pick two points on the curve. Draw a straight line through these two points. If the line has a positive slope, then you have a growth function. If the line has a negative slope, then you have a decay function.
Visually, a growth function will move upwards as you move from left to right.
In contrast, a decay function will move downwards as you move from left to right.


The graph in blue represents a growth function. The green graph is a decay function. 
{{{ graph( 500, 500, -10, 10, -10, 10, 0, 2(0.55)^x, 3(1.2)^x) }}}

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b) If {{{0 < b < 1}}}, then the function decays. If {{{ b > 1 }}}, then you have a growth function.


For instance, {{{y = 2(0.3)^x}}} is a decay function (since b = 0.3 is between 0 and 1). As x gets bigger, y gets smaller.


Another example: {{{y = 5(8)^x}}} is a growth function (b = 8 makes b > 1 true). As x gets bigger, y gets larger as well.
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