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if you rearrange the table you find that it has a common difference of 3/4

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The total perimeter increases by 6 units each time if the side of each square equals one unit.

Equal differences over equal intervals.

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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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If the pattern is arithmetic or geometric there will be an equal change from one term to the next. They are similar because the all either increase or decrease by a common number. They are different because they either increase or decrease by different amounts and either grow exponentially or equally.

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neither
pattern= n x n (it's n squared but we don't know how to make a tiny 2)

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Equal factors over equal
intervals

Since we learned recursive formulas we know that whatever f(n-1) is multiplied by is the common ratio, and since it's being multiplied it is geometric.

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Equal factors over equal intervals because the algae grows 3% each year.
Common ratio is 1.03.

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NEITHER
Intervals are equal but it's not a function

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It's geometric and it divides by 2 every time. We found the pattern of change by looking at the graph.

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This pattern has equal differences over equal intervals. This pattern is arithmetic. We found the pattern of change, which is 2, by finding the change of f(x) and dividing it by the change of x. In this case, f(x) changed by 10 and x changed by 5.

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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 3

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Group 5

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Group 6

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Group 4

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Group 1

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Group 9

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Group 7

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Group 2