Formulas For Linear Functions. Can Anyone Me Understand This Problem?

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Discussion Overview

The discussion revolves around a problem related to linear functions, specifically focusing on the earnings of an insurance salesperson. Participants explore the formulation of the function representing annual earnings, including the identification of slope, y-intercept, and the equation itself. The scope includes mathematical reasoning and clarification of terminology.

Discussion Character

  • Homework-related, Mathematical reasoning, Conceptual clarification

Main Points Raised

  • One participant expresses difficulty in solving the problem and presents an initial function for annual earnings as 12000 + 0.03X.
  • Another participant confirms that the proposed equation is correct and indicates that it contains answers to the questions posed.
  • A third participant points out that the expression provided is not an equation due to the absence of an equals sign, suggesting it should be referred to as a function or expression instead.
  • A later reply emphasizes the need to clarify what 'x' represents, presuming it to be the value of premiums sold, and raises concerns about the rigor of the problem given the discrete nature of the quantities involved.

Areas of Agreement / Disagreement

Participants generally agree on the correctness of the initial function presented, but there is disagreement regarding the terminology used and the rigor of the problem itself. The discussion remains unresolved regarding the appropriateness of the problem's formulation.

Contextual Notes

There are limitations regarding the assumptions about the nature of 'x' and the treatment of the quantities as discrete, which may affect the interpretation of the problem.

dmbeluke
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I am stuck. I've gone through all my notes to try and figure out how to do this problem, with no success. Any help would be appriciated. Thank you!


An insurance salesperson earns an annual salary of $12,000 plus a commission equal to 3% of the premiums on all policies sold. If f(x) is a function which gives her annual earnings, what is the slope of f(x)? What is the y-intercept? Find the equation for f(x).


The equation I came up with was:
12000+.03X

This is as far as I have gotten.
 
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Hint

Your equation is correct.

Note the two numbers in your equation. One of them is the answer to one of the questions, and the other is the answer to the other question.
 
Just a minor detail:
12000+.03X is not an "equation" (there's no 'equals' sign on it).
You can call it a function , or an expression.
 
You also ought to specify what x is (we presume it is the value of the premiums she sells).

Then of course I'd like to argue that seeing as these quantities are all discrete (she preusmably doesn't sell 120,000.02939430854324359 worth of premiums in whatever currency we're dealing with, and she'll have a funny bank account that goes to more than two decimal places) that the question ought to be excised from the book/homework sheet as being not particularly rigorous.
 

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