SOLUTION: 1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by {{{C=6000/(200-2x)}}} a. What is the cost to remove 75% of the pollutant? b. What is t

Algebra ->  Graphs -> SOLUTION: 1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by {{{C=6000/(200-2x)}}} a. What is the cost to remove 75% of the pollutant? b. What is t      Log On


   

Question 140635: 1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C=6000%2F%28200-2x%29

a. What is the cost to remove 75% of the pollutant?
b. What is the cost to remove 90 % of the pollutant?
c. What is the cost to remove 99% of the pollutant?
d. For what value is this equation undefined?
e. Do the answers to sections a–d match your expectations? Why or why not?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)

C=6000%2F%28200-2x%29 Start with the given equation


C=6000%2F%28200-2%2875%29%29 Plug in x=75


C=6000%2F%28200-150%29 Multiply


C=6000%2F%2850%29 Subtract


C=120 Divide


So the cost is 120 million dollars to remove 75% of the pollutant (remember C is in millions of dollars)


-------------------------------------------------------------


b)

C=6000%2F%28200-2x%29 Start with the given equation


C=6000%2F%28200-2%2890%29%29 Plug in x=90


C=6000%2F%28200-180%29 Multiply


C=6000%2F%2820%29 Subtract


C=300 Divide


So the cost is 300 million dollars to remove 90% of the pollutant (remember C is in millions of dollars)


-------------------------------------------------------------




c)

C=6000%2F%28200-2x%29 Start with the given equation


C=6000%2F%28200-2%2899%29%29 Plug in x=99


C=6000%2F%28200-198%29 Multiply


C=6000%2F%282%29 Subtract


C=3000 Divide


So the cost is 3,000 million dollars, or 3 billion dollars, to remove 99% of the pollutant (remember C is in millions of dollars)


-------------------------------------------------------------


d)

C=6000%2F%28200-2x%29 Start with the given equation


200-2x=0 Set the denominator equal to zero. Remember, dividing by zero is undefined.


200=2x Add 2x to both sides


100=x Divide both sides by 2


So when x=100 this means that the entire denominator will be equal to zero. So x=100 makes the equation undefined.


-------------------------------------------------------

e)

It's entirely plausible since it becomes harder and harder to clean 100% of the mess.