Question 178411

a)


{{{C(p)=(500000)/(100-p)}}} Start with the given function



{{{C(90)=(500000)/(100-90)}}} Plug in {{{p=90}}}



{{{C(90)=(500000)/(10)}}} Subtract



{{{C(90)=50000}}} Divide



So it costs $50,000 to remove 90% of the toxic chemicals.


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{{{C(p)=(500000)/(100-p)}}} Start with the given function



{{{C(95)=(500000)/(100-95)}}} Plug in {{{p=95}}}



{{{C(95)=(500000)/(5)}}} Subtract



{{{C(95)=100000}}} Divide



So it costs $100,000 to remove 95% of the toxic chemicals.



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b)



{{{C(p)=(500000)/(100-p)}}} Start with the given function



{{{C(99.5)=(500000)/(100-99.5)}}} Plug in {{{p=99.5}}}



{{{C(99.5)=(500000)/(0.5)}}} Subtract



{{{C(99.5)=1000000}}} Divide



So it costs $1,000,000 to remove 99.5% of the toxic chemicals.



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{{{C(p)=(500000)/(100-p)}}} Start with the given function



{{{C(99.9)=(500000)/(100-99.9)}}} Plug in {{{p=99.9}}}



{{{C(99.9)=(500000)/(0.1)}}} Subtract



{{{C(99.9)=5000000}}} Divide



So it costs $5,000,000 to remove 99.9% of the toxic chemicals.



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c)


As the percentage approaches 100, the cost increases dramatically. Notice how the cost increased tenfold (ie multiplied by 10) as "p" changed from 95 to 99.5


Also, take note that "p" CANNOT be equal to 100. If p was equal to 100, then there would be a division by zero (which is undefined). So this means that we CANNOT completely remove the toxic chemicals.