Question 69234: Include the following in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
Give real-life examples of both arithmetic and geometric sequences and series. Explain how these examples might affect you personally.
Answer by Nate(3500)   (Show Source):
You can put this solution on YOUR website! Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?
Let's use an example:
2,4,6,8,10,12,14,16,etc.
First Digit = 2
Second Digit = 4
(1,2) and (2,4)
m = 2/1
y = 2x
x = 3
y = 6
The line is linear.
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
Let's use an example:
1,3,9,27,81,etc.
(1,1) and (2,3)
m = 2/1
y = 2x - 1
x = 3
y = 5 the value should be 9
Not Linear
Quadratic? what is the vertex? let's leave that
Exponential?
(0,1/3)
y = a*b^x
1/3 = a*1
y = (1/3)b^x
1 = (1/3)b
3 = b
y = (1/3)(3^x) = 3^(x - 1)
x = 3
y = 3^2 = 9
The line is exponential.
The rest is self explanatory.
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