SOLUTION: How do you determine if a function has growth or decay... a) when looking at a graph? b)when looking at an equation y=a(b)^t?

Algebra ->  Rational-functions -> SOLUTION: How do you determine if a function has growth or decay... a) when looking at a graph? b)when looking at an equation y=a(b)^t?      Log On


   

Question 1090792: How do you determine if a function has growth or decay...
a) when looking at a graph?
b)when looking at an equation y=a(b)^t?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+0%2C+2%280.55%29%5Ex%2C+3%281.2%29%5Ex%29+
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b) If 0+%3C+b+%3C+1, then the function decays. If +b+%3E+1+, then you have a growth function.

For instance, y+=+2%280.3%29%5Ex is a decay function (since b = 0.3 is between 0 and 1). As x gets bigger, y gets smaller.

Another example: y+=+5%288%29%5Ex is a growth function (b = 8 makes b > 1 true). As x gets bigger, y gets larger as well.