Question 122545
 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.
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Assuming you mean:
C(x)= {{{1.5x/((100-x))}}}
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Using this model, approximately what is the cost if 60% of the citizens participate?
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Just substitute 60 for x in the given equation
C(x)= {{{1.5(60)/((100-60))}}}
C(x)= {{{90/40}}}
C(x) = 2.25 million$
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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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Replace C(x) with 5, and solve for x:
5 = {{{1.5x/((100-x))}}}
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Multiply both sides by (100-x) and you have:
5(100-x) = 1.5x
500 - 5x = 1.5x
500 = 1.5x + 5x; added 5x to both sides:
500 = 6.5x
x = 500/6.5
x = 77% participate when $5 million is spent
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Check solution find C(x) when x = 77%
C(x)= {{{1.5(77)/((100-77))}}}
C(x)= {{{115.5/23}}}
C(x)= 5.02 ~ 5; confirms our solution
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