Don't understand the cost of implementing a city recycling project?

  • Context: High School 
  • Thread starter Thread starter poohbear1986
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Discussion Overview

The discussion revolves around understanding the cost function for implementing a city recycling project based on citizen participation rates. Participants explore how to evaluate the cost function C when a certain percentage of citizens, specifically 60%, participate, and how to determine the participation percentage corresponding to a fixed budget of $5 million.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about calculating the cost C when 60% of citizens participate, asking for clarification on the function.
  • Another participant requests a definition of the function C and suggests that more information is needed to solve the problem.
  • A participant provides the formula C(x) = 1.5x/(100-x) as given in their textbook.
  • Several participants attempt to substitute x with 60 in the formula to compute C(60), with varying interpretations of the calculations.
  • One participant questions the validity of dividing the result by 60, leading to a discussion about the notation C(x) and its meaning as a function rather than multiplication.
  • Ultimately, a participant concludes that the cost is 2.25 million dollars after resolving their confusion about the calculations.

Areas of Agreement / Disagreement

There is no consensus on the correct interpretation of the function notation and the calculations involved. Participants express differing views on how to manipulate the function and arrive at the cost.

Contextual Notes

Participants have not fully resolved the assumptions regarding the function's definition and the implications of the calculations, leading to some confusion about the mathematical steps involved.

poohbear1986
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dont understand

For the following function, C computes the cost in millions of dollars of implementing a city recycling project when x percent of the citizens participate.
Using this model, approximately what is the cost if 60% of the citizens participate?
Using this model, estimate the percentage of participation that can be excepted if $5 million is spent on this recycling project? Set up an equation and solve algebraically. Round to the nearest whole percent
 
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Do you have a function definition for C? Do you have sufficient information to find the function C?

Your information seems to become:
C=f(x); what is f(0.60)? what is x when 5=f(x)?... in other words, if C=5, what is f(x)?

More information is needed.
 
C(x)=1.5x/100-x

his is the formula the book gives me
 
So x is the percentage and C is the total cost.

Replace x with 60 in the formula and see what C is.
 
i did that a got like .04 but to me that doesn't seem right
 
poohbear1986 said:
i did that a got like .04 but to me that doesn't seem right

I assume the formula to mean this:

C(x)=(1.5x)/(100-x)

Right? In which case put 60 in and work out again.
 
this is what i did
C(X)=1.5X/100-X
C(60)=1.5*60/100-60
C(60)=90/40
C(60)=2.25
C(60/60)=2.25/60
C=.0375 OR .04
so I'm suppose to put this in millions if i move the decimal point over six spaces then i get37,500 or 40,000
 
poohbear1986 said:
C(60)=2.25
C(60/60)=2.25/60

I don't understand why you suddenly decided to divide it by 60 here, I also don't understand why you think: C(x/60) = C(x)/60
 
isnt the x in front of the C a 60 so to get C by itself you divide
 
  • #10
poohbear1986 said:
isnt the x in front of the C a 60 so to get C by itself you divide

No it isn't. The notation C(x) means that C is a function of x, it is not multiplication of C by x. Often in math we use a shorthand and refer to a function f(x) by merely f, that is what is happening when they ask you for the value of C whe x=60, or C(60), that is the function C(x) evaluated at the number 60, not C "times" 60.
 
  • #11
ok i think i get it now, so my answer would be 2.25, put that into millions and i get 2,250,000
 

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