Function help

Question

A cost-benefit function C computes the cost, in millions of dollars, of implementing a city recycling project where x percent of the citizens participate, where. C(x)=x/100-x



a) If 75 percent participation is expected, determine the cost for the city recycling project.

b) The city plans to spend $5 million on this project. Estimate the percentage of participation that can be expected.

Answer 1

If x refers to the percent then x=75. 

a. An important note to make here is that the functions should read C(x)= x/(100-x) otherwise a negative result would occur and that doesn't make sense in the context of the question. 

with x=75,

C(75)=75/(100-75)=75/25=3

where 3 is in millions of dollars.

b. the cost is 5 million dollars and C(x) is in millions of dollars so C(x)=5.

this leads to:

C(x)=5=x/(100-x)

5(100-x)=x by multiplying each side by (100-x)

500-5x=x by distributing the 5 to each term

500=6x by adding 5x to both sides

500/6=x by dividing 6 by both sides

83.33=x (approximately) where x is the percentage of citizens who participated.