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Janet wants to know how many seats are in each row of the theater. Jamal lets her know that each row has 2 seats more than the row in front of it. The first row has 14 seats. Is this relationship linear, exponential, or neither?​

User Ken Kinder
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1 Answer

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Final answer:

The pattern described by Jamal, where each row has 2 seats more than the row in front of it, starting with 14 seats in the first row, represents a linear relationship. This is because the number of seats increases by a constant amount, not by a multiplying factor, for each new row.

Step-by-step explanation:

Let's analyze the situation with Janet and Jamal. The number of seats in each subsequent row is increasing by a constant amount, specifically 2 more than the row before it. This kind of pattern represents a linear relationship. The first row has 14 seats, and if each subsequent row has 2 more seats than the row before it, the second row would have 16, the third would have 18, and so on. The number of seats in the nth row can be calculated using the formula: Seats in nth row = 14 + (n - 1) × 2.

As you can see, this formula dictates a linear increase in the seats because for every additional row, we are simply adding 2 to the previous total. This is not an exponential relationship as the increase is not multiplying by a constant factor. The number of seats does not double or increase by a percentage with each new row; it increases by a constant number. This is the defining characteristic of a linear relationship.

User Henry Liu
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