For the following function, C computes the cost in millions of dollars of implementing a city recycling?

project c(x)=1.3x/100-x


A)Using this model, approximately what is the cost if 40% of the citizens participate? Include units with your answer.





B)Using this model, estimate the percentage of participation that can be excepted if $3 million is spent on this recycling project? Set up an equation and solve algebraically. Round to the nearest whole percent.

For the following function, C computes the cost in millions of dollars of implementing a city recycling?
Part A





C(x) = (1.3x)/(100-x) [in millions of dollars]





They want you to approximate the cost if 40% of the citizens participate. So... they are giving you "x"... which is 40%





So... all you have to do is plug in "40" for "x" ... to find "C"





C(x) = (1.3x)/(100-x) ... becomes...





C(when x = 40) = (1.3)(40)/(100-40)





C(x = 40) = 52/60 = 0.8666666.... (but remember that this is 0.86666666 OF $1,000,000.... so you need to multiply the 0.8666666 by $1,000,000....





So.... If 40% of the citizens participate, the recycling project will cost $866,667..... because (0.8666666)($1,000,000) = $866,667





PART B





C(X) = (1.3x)/(100-x) [in millions of dollars]





They tell you that the Cost C = $3 million





So....





C(X) = (1.3x)/(100-x) .... becomes...





3 = (1.3x)/(100-x)





Now solve for "x"...





First multiply the equation through by (100-x)...





You'll get...





3(100-x) = (1.3x)





Now distribute the "3" to the "100"... and the "-x"....





3(100) + (3)(-x) = 1.3x





300 - 3x = 1.3x





Add "3x" to both sides... like this...





(300 - 3x) + 3x = 1.3x + 3x





Combine "like" terms... and you get...





300 = 4.3x





.... which is the same as writing....





4.3x = 300





Now divide both sides by 4.3... like this...





4.3x .... 300


------ = --------


4.3 ....... 4.3





The 4.3's on the left side cancel each other out... leaving you with...





x = 300/4.3 = 69.767%





So.... if $3 million is spent on this recycling project, citizen participation is roughly 70%