Exponential Function Models Worksheet With Answers
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7Math 117 Lecture 9 notes page 1
Exponential Function Models
Arithmetic sequences are modeled by polynomial functions:
2
or
Linear: y = mx + b
quadratic: y = ax
+ bx + c
By examining a table of ordered pairs, you'll notice that as x increments by a constant, either the first
of second differences of y increases by a constant difference. This is characteristic of arithmetic
sequences.
Geometric sequences are modeled by exponential functions:
x
y = a•b
where b = constant ratio and a is a constant
By examining a table of ordered pairs, you'll notice that as x increments by a constant, the value of y
increases by a common ratio. This is characteristic of geometric sequences.
x
y
x
y
x
y
–3
–3
–3
11
–3
3
–2
–1
–2
6
–2
6
–1
3
–1
12
–1
1
0
2
0
24
0
3
1
3
1
48
1
5
2
7
2
6
2
96
3
9
3
11
3
182
Some organizations need to spread information accurately to many people quickly. So, telephone calling
trees often are used by the organization. (diagram on overhead)
Stage
1
2
3
4
5
6
7
8
9
10
Members
1
2
4
8
16
32
64
128
256
512
Output is doubled in each stage.
In data plot, output value doubles for each move of 1 unit on x-axis.
This is a geometric sequence where the constant ratio is 2.
Geometric sequences are modeled by exponential functions:
x
y = a•b
where b = constant ratio and a is a constant
For this particular data, b = 2.
Using any ordered pair in the data, such as (1,1)
1
1 = a•2
which tells us that a = 1/2
x
So the model for this data is: y = (1/2)•2
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