Step 1 :Given the cost function \(C(p)=\frac{40,000}{100-p}\), we are asked to find the cost of removing certain percentages of pollutants.
Step 2 :Substitute \(p=0\) into the function to find \(C(0)\), which gives \(C(0)=\frac{40,000}{100-0} = \$400\).
Step 3 :Substitute \(p=20\) into the function to find \(C(20)\), which gives \(C(20)=\frac{40,000}{100-20} = \$500\).
Step 4 :Substitute \(p=80\) into the function to find \(C(80)\), which gives \(C(80)=\frac{40,000}{100-80} = \$2000\).
Step 5 :Substitute \(p=90\) into the function to find \(C(90)\), which gives \(C(90)=\frac{40,000}{100-90} = \$4000\).
Step 6 :Final Answer: \(C(0)=\boxed{\$400}\), \(C(20)=\boxed{\$500}\), \(C(80)=\boxed{\$2000}\), and \(C(90)=\boxed{\$4000}\).