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- they all have a pattern of change
- some are arithmetic and some are geometric
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Linear Function: Similar pattern to arithmetic Sequences, but is classified as a function.  This has equal differences over equal intervals. (Known as the slope)

Exponential Function: Similar pattern to Geometric Sequences, but is classified as a function. This has equal factors over equal intervals. (Exponential Graphs do NOT have a constant Slope

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We divided the change in f(x) by the change in x and found that it was 3/4 every time (or 0.75).

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How I found the pattern of change:
We counted the perimeter, and we found out that for every stage, there is a 6 unit increase for the perimeter.

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How we found the rate of change was by noticing that when x increased by 5, f(x) increased by 10. That means f(x) is 2x, with a y-intercept of three as 0x equals 3x.

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Since each square has a length of 1 unit, the area of one square would be 1 unit squared. Because of this, we calculated the area of each step and found that the initial change is 3 from step 1 to 2, then it increases by 2 each time. (Change: +3,+5,+7...)

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Equal factors over equal intervals. We know this because we are constantly multiplying by 5/3

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Equal factors over equal intervals. We know this because we are constantly multiplying by 5/3

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By looking at the graph, you can see that the rate of change between intervals is 1/2, which is a common factor not a common difference

f(n)=160(1/2)^n

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The main concept/idea  is to identify between three different types of patterns, and explain how you found them. We noticed that each pattern had a Pattern of change and they had  equal factors over equal intervals, equal differences over equal intervals, or neither.

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How we found the pattern of change: Group 1 noticed that there was no change of x-values which would cause the line to have an undefined slope.

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This pattern is an example of "Equal factors over equal intervals."
The pattern is stated in the statement (3% or 1.03). Each term is multiplied by some form of 1.03.

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Summary: What do you notice about all of these patterns?  What is similar and what is different?

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Summary: What do you notice about all of these patterns?  What is similar and what is different?

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Group 8

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Group 5

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Group 2

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Group 7

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Group 3

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Group 9

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Group 1

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Group 6

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Group 4