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Sketch the graph of the function defined by the given equation.$$y=f(x)=\left(\frac{e}{3}\right)^{x}.$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

The Number $e$

Oregon State University

McMaster University

Idaho State University

Lectures

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Sketch the graph of the fu…

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Sketch a graph of the give…

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02:24

Yeah, eso The premise of this problem is understanding the difference between growth and decay because both of these exponential functions are of the form B to the X. The difference, though, is in growth. The base is larger than one, whereas indicated the basis less than one, you know, or bigger than zero. And some people will put absolute value in there. But we don't have to worry about this because we're looking at e divided by three to the X power. So all we're examining is a positive value of E over three. Which E is about 2.718 Use the calculator to check that value divided by three. And when the numerator is smaller than the denominator, we know that that number is going to be less than one. So we're looking at exponential decay in this problem, which tells me that dysfunction yeah, is going down into the right because that's what decay does. Um, and if you wanted to, you could still put the y intercept of 01 in here. That's not really what they care about. They care that you understand what needs to happen for this to be exponential decay

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