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GREYUIT [131]
2 years ago
13

Which table represents an exponential function of the form y = b^k when 0 < b < 1?

Mathematics
2 answers:
sladkih [1.3K]2 years ago
6 0

Answer:

Answer is B

Step-by-step explanation:

Just got it right

IceJOKER [234]2 years ago
6 0

Answer:

Table 2 is the right representation of exponential functio.

Step-by-step explanation:

We are given the following information in the question:

y = b^k,\\0

If we look at table 2, then, the exponential function is of the form:

y(x) = \bigg(\displaystyle\frac{1}{3}\bigg)^x

Putting different values of x, we have:

x = -3\\\\y(-3) = \bigg(\displaystyle\frac{1}{3}\bigg)^{-3} = 27\\\\x = -2\\\\y(-2) = \bigg(\displaystyle\frac{1}{3}\bigg)^{-3} = 9\\\\x = -1\\\\y(-1) = \bigg(\displaystyle\frac{1}{3}\bigg)^{-1} = 3\\\\x = -0\\\\y(0) = \bigg(\displaystyle\frac{1}{3}\bigg)^{0} = 1\\\\x = 1\\\\y(1) = \bigg(\displaystyle\frac{1}{3}\bigg)^{1} = \frac{1}{3}\\\\x = 2\\\\y(2) = \bigg(\displaystyle\frac{1}{3}\bigg)^{2} = \frac{1}{9}\\\\x = 3\\\\y(3) = \bigg(\displaystyle\frac{1}{3}\bigg)^{3} = \frac{1}{27}\\

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<h2>Hello!</h2>

The answer is:

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<h2>Why?</h2>

To solve this problem, first we need to derivate the given function, and then, evaluate the derivated function with x equal to 2.

The given function is:

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It's a quotient, so, we need to use the following formula to derivate it:

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Then, of the given function we have that:

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f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*(4)'-4*(x)'}{x^{2} }

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f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{0-4}{x^{2} }

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Have a nice day!

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