This task requires a minimum of 3 separate responses. An equation (1) describes,

Question

This task requires a minimum of 3 separate responses.   An equation (1) describes, (2) balances, or (3) shows the relationship of how things vary between an independent and a dependent variable.        For this discussion board, let's assume that the dependent variable initially grows at a fairly fast rate and then there is a very slow growth rate as time continues to increase and approach infinity.  

Part 1:   Which of the three terms gives an 'equation' the most meaning to you.   Or is there another term that comes to mind when hear the word 'equation'.    Give a short discussion of the term you picked and why.

Part 2: Post or list a potential equation with use of appropriate variables that satisfies the verbal description between the variables given in the discussion board statement above.     Present the equation and give a short discussion of how it answers the relationship between the variables and state why you picked it.

Part 3:   Post a response or interact with at least one of your peer's entries prior to the end of the week (by next Tuesday evening).    At a minimum, state why you agree with or disagree with their input.

Explanation / Answer

Part 1: An equation "Describes" the relationship of how things vary between an independent and a dependent variable.

"Balancing" cannot be a sole definition of an equation as this is one of the property of an equation.

To me "Describe" is more meaningful becuase through an equation we not only see the relationship between an independent and a dependent variable, but also we can make some inferrential judgements by applying many more mathematical operations. Hence, in short an equation is not just an image to be shown, it also describes many hidden facts that we can deduce or infer if we deep dive into the relationship described. Hence, in my accordance "Description" of the relationship will be more firm definition of "AN EQUATION".

Part 2:

Let us post the following example of an equation where the dependent variable initially grows at a fairly fast rate and then there is a very slow growth rate as the time continues to increase and approaches infinity:

y = a + b ln(x) , where "y" is dependent variable and "x" is independent variable, b > 0.

Here, if we choose any arbitrary value of the coefficients "a" and "b" and if we keep increasing the value of "x", the value of "y" will firstly increase at a high rate and then after some time the growth will get slow.

To illustrate, let us consider a = 2 and b = 5.

Hence, clearly we can see that "y" first increases at high rate and the the rate decreases.

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