2016­12­14 Exponential growth or Decay from a graph or Table.notebook December 14, 2016
Tuesday,
12/14/2016
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Text Pg 319: 5-47 (odd)
Homework:
2016­12­14 Exponential growth or Decay from a graph or Table.notebook December 14, 2016
Exponential Functions:
y = a (b)x
Standard form:
Initial Value
Exponent
Base / Growth (or Decay) Factor
Growth (or Decay) rate is given by |b - 1|
If b < 1, we say that the function models exponential decay
If b > 1, we say that the function models exponential growth
Determine if the following display exponential growth or
decay?
1)
4)
3)
2)
5)
2016­12­14 Exponential growth or Decay from a graph or Table.notebook December 14, 2016
Given the formula, determine if the function shows growth or decay, the
growth/ decay factor, growth/ decay rate, and initial value:
Growth or Decay:
Growth/Decay Factor:
Growth/Decay Rate:
Initial Value:
Growth or Decay:
Growth/Decay Factor:
Growth/Decay Rate:
Initial Value:
Growth or Decay:
Growth/Decay Factor:
Growth/Decay Rate:
Initial Value:
Growth or Decay:
Growth/Decay Factor:
Growth/Decay Rate:
Initial Value:
Creating the equation for an exponential function
from a table.
From out Geometric Sequences, we know that exponential
functions have a common ratio, between consecutive
outputs. That ratio is our b value.
x y
0 2
1 6
2 18
3 48
Our initial value, a, is found when x = 0!
y = a (b)x
* Note: Always divide next output by previous output.
2016­12­14 Exponential growth or Decay from a graph or Table.notebook December 14, 2016
Practice:
2) x
1) x
y
0 5
1 15
2 45
3 135
3) x y
0
1
2 -72
3 -432
0
1
2
3
4
4)
x y
0
1
2 1
3 .5
y
.5
2
8
32
128