The cost C(x) (in $1000) for a city to remove x% of the waste from a polluted river is given by [tex]C(x)=\frac{80x}{100-x}[/tex]a. Determine the cost to remove 20%, 40%, and 90% of the waste. Round to the nearest thousand dollars.b. If the city has $320,000 budgeted for river cleanup, what percentage of the waste can be removed?

Answer:a) 20,000$ is the cost to remove 20% of waste from polluted river.53,334$ is the cost to remove 40% of waste from polluted river.720,000$ is the cost to remove 90% of waste from polluted river. b) 80% of the waste can be removed.                 Step-by-step explanation:We are given the following information in the question:The cost C(x) (in $1000) for a city to remove x% of the waste from a polluted river is given by:[tex]C(x) = \displaystyle\frac{80x}{100-x}[/tex]a) x = 20%[tex]C(20) = \displaystyle\frac{80(20)}{100-20} = 20[/tex]20,000$ is the cost to remove 20% of waste from polluted river.x = 40%[tex]C(40) = \displaystyle\frac{80(40)}{100-40} \approx 50.334[/tex]Approximately, 53,334$ is the cost to remove 40% of waste from polluted river.x = 90%[tex]C(90) = \displaystyle\frac{80(90)}{100-90} = 720[/tex]720,000$ is the cost to remove 90% of waste from polluted river.b) The city has $320,000 budgeted for river cleanup.[tex]C(x) = 320\\320 = \displaystyle\frac{80x}{100-x}\\\\320(100-x) = 80x\\32000 - 320x = 80x\\400x = 32000\\x = 80[/tex]Thus, 80% of the waste can be removed.