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

[poohbear1986]

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

 

[symbolipoint]

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.

 

[poohbear1986]

C(x)=1.5x/100-x

his is the formula the book gives me

 

[Zurtex]

So x is the percentage and C is the total cost.

Replace x with 60 in the formula and see what C is.

 

[poohbear1986]

i did that a got like .04 but to me that doesn't seem right

 

[Zurtex]

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.

 

[poohbear1986]

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

 

[Zurtex]

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

 

[poohbear1986]

isnt the x in front of the C a 60 so to get C by itself you divide

 

[d_leet]

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.

 

[poohbear1986]

ok i think i get it now, so my answer would be 2.25, put that into millions and i get 2,250,000