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pentagon [3]
3 years ago
10

Is this relationship linear, exponential, or neither ?

Mathematics
1 answer:
Dovator [93]3 years ago
6 0

Exponential

Step-by-step explanation:

So let’s start off by looking at how much x is growing by each time

X is growing by 8 each time

Next look at how much y is growing by

-6 to -24 is a difference of 18

-24 to -96 is a difference of 72

And lastly -96 to -384 is a difference of 288

So we can now say that it is not linear because a linear equation grows by a constant number (like adding)

To determine if it is exponential see if it is growing by a constant multiplier

24 divided by 6 is 4

96 divided by 24 is 4

384 divided by 96 is 4

It is exponentially growing by 4

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Answer:

(27 y^(-8))/(4 x^6)

Step-by-step explanation:

Simplify the following:

(4 (3 x^2 y^4)^3)/(2 x^3 y^5)^4

Multiply each exponent in 2 x^3 y^5 by 4:

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4×3 = 12:

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2^4 = (2^2)^2:

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2^2 = 4:

(4 (3 x^2 y^4)^3)/(4^2 x^12 y^20)

4^2 = 16:

(4 (3 x^2 y^4)^3)/(16 x^12 y^20)

Multiply each exponent in 3 x^2 y^4 by 3:

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3×4 = 12:

(4×3^3 x^(3×2) y^12)/(16 x^12 y^20)

3×2 = 6:

(4×3^3 x^6 y^12)/(16 x^12 y^20)

3^3 = 3×3^2:

(4×3×3^2 x^6 y^12)/(16 x^12 y^20)

3^2 = 9:

(4×3×9 x^6 y^12)/(16 x^12 y^20)

3×9 = 27:

(4×27 x^6 y^12)/(16 x^12 y^20)

4/16 = 4/(4×4) = 1/4:

(27 x^6 y^12)/(4 x^12 y^20)

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(27 x^(-6) y^(12 - 20))/4

12 - 20 = -8:

Answer: (27 y^(-8))/(4 x^6)

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