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Is the following linear, exponential, or neither? 3,6,9,12,15,18...

User Ronon
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2 Answers

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Final answer:

The sequence described is an example of a linear relationship since there is a constant rate of change, characterized by adding the same number to each term. It is not exponential, as exponential growth is multiplicative rather than additive.

Step-by-step explanation:

The sequence of numbers given, 3, 6, 9, 12, 15, 18..., can be characterized by recognizing the pattern in the differences between consecutive terms. In this case, each term is increased by 3 to get the next term (6-3=3, 9-6=3, etc.) which suggests a consistent rate of change.

This pattern is indicative of a linear relationship, which in mathematical terms, is expressed in the form of a linear equation y = mx + b, where m is the constant rate of change (the slope) and b is the y-intercept. For example, using this sequence, if each number represents the y-value corresponding with integral x-values (1 for 3, 2 for 6, 3 for 9, etc.), the equation for this pattern would be y = 3x ('b' equals zero since the sequence passes through the origin).

Meanwhile, exponential growth is characterized by a growth rate that is a constant percentage or fraction of the current amount, often seen in formulas like y = a × b^x, where a is the initial amount, b is the base or growth factor, and x is the time or sequence number. The essential feature of exponential growth is multiplicative, not additive, and on a logarithmic plot, exponentials would become straight lines due to their multiplicative nature.

User J Weezy
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Given:

3,6,9,12,15,18...

We need to find the difference.

The difference between 3 and 6 is 6-3 =3.

The difference between 6 and 9 is 9-6 =3.

The difference between 9 and 12 is 12-9 =3.

The difference between 12 and 15 is 15-12 =3.

The difference between 15 and 18 is 18-15 =3.

Recall that linear have equal differences.

We get an equal difference between each value.

The form of the equation is


y=3x

Hence the given is linear.

User Nero
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