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.
