SOLUTION: 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. C(x)=1.4/(100-x)

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Question 113705: 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.
C(x)=1.4/(100-x)
a) Using this model, approximately what is the cost if 60% of the citizens participate?
b) Using this model, estimate the percentage of participation that can be excepted if $4 million is spent on this recycling project. Set up an equation and solve algebraically. Round to the nearest whole percent.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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.
C(x)= 1.4x%2F%28100-x%29
:
A) using this model, approximately what is the cost if 60% of the citizens participate. answer and show work
:
Substitute 60 for x in the above equation, find C(x)
C(x)= 1.4%2860%29%2F%28100-60%29
:
C(x)= 84%2F%2840%29
:
C(x) = 2.1 million dollars when 60% participate
:
:
B) using this model estimate the percentage of participation that can be excepted if $4 million is spent on this recycling project. Set up an equation and solve algebraically. Round to the nearest whole percent.
:
1.4x%2F%28100-x%29 = 4: substituted 4 for C(x)
:
Multiply equation by (100-x) to get rid of the denominator:
1.4x = 4(100 - x)
:
1.4x = 400 - 4x
:
1.4x + 4x = 400
:
5.4x = 400
:
x = 400/5.4
:
x = 74% participation when 4 million is spent