A: Which has a greater rate of change?
B: How can you tell

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Ответ:

gsbsjshzn

05.10.2021

Mathematics

Option D : 3 Superscript negative x Baseline = 3 Superscript 3 x + 6

Step-by-step explanation:

Let us first convert all the equations in Mathematical form for readability.

The question equation will become:

$(\frac{1}{3})^{x}=(27)^{x+2}$ ----------------- (1)

And the option equations will be:

A. $3^{x}=3^{(-3x+2)}$

B. $3^{x}=3^{(3x+6)}$

C. $3^{-x}=3^{(3x+2)}$

D. $3^{-x}=3^{(3x+6)}$

Now, let's solve the question equation. Simplifying equation (1), we get

$(3^{-1})^{x} = (3^3)^{x+2}\\\\3^{-x} = 3^{3(x+2)}\\\\3^{-x} = 3^{(3x+6)}$

Hence, option D is correct.

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A: Which has a greater rate of change? B: How can you tell