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Zolol [24]
3 years ago
15

What are some similarities and differences of the rates of change of linear, quadratic, and exponential functions?

Mathematics
1 answer:
gregori [183]3 years ago
5 0

Answer:

linear functions change a constant rate. i.e. the slope of the graph is constant.

d/dx (mx+b) = m


quadratic functions change at a linear rate, slower than the function itself.

The slope of the tangent to the graph is proportional to the x coordinate.

d/dx (ax^2) = 2ax

Slope of tangent to ax^2 at point (x,ax^2) is 2ax.


Exponential functions change at the same rate as the function itself. The slope of the tangent to the graph is proportional to the y coordinate.


The slope of tangent at point (x,exp(x)) is exp(x).


Definition of exp(x) is just exp(0) = 1 and d/dx exp(x) = exp(x).


d/dx exp(ax) = a exp(ax) is not part of the definition, but follows from from the chain rule


Step-by-step explanation:


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Kelley writes the expression n 2 to model the phrase "xander studied two more hours than nandini." which best explains the accur
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It is accurate. In the phrase “two more hours than Nandini,” n + 2 are correct translations. Then the correct option is A.

<h3>What is Algebra?</h3>

Algebra is used to analyze mathematical symbols, and logic is used to manipulate those symbols.

As an example, Kelley models the sentence "Xander studied two more hours than Nandini" using the equation n + 2.

Consequently, the following will describe Kelley's expression's accuracy the best:

It is precise. Since "two" is translated as "2," "more" as "+," and "Nandini's study time is unknown or "n," 2 + n or n + 2 are the appropriate translations for the sentence "two more hours than Nandini."

So, option A is the best choice.

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I understand that the question you are looking for is :

Kelley writes the expression n + 2 to model the phrase “Xander studied two more hours than Nandini.” Which best explains the accuracy of Kelley’s expression?

It is accurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n or n + 2 are correct translations.

It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n is the correct translation.

It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “>,” and Nandini’s study time is unknown or “n,” so 2 greater-than n is the correct translation.

It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “<,” and Nandini’s study time is unknown or “n,” so 2 less-than n is the correct translation.

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