a city's main well was recently found to be contaminated with trichloreathylene (a cancer-causing chemical) as a result of an abandoned chemical pump that leached chemicals into the water. a proposal submitted to the city council indicated that the cost, in millions of dollars, of removing x% of the toxic pollutants is
.05x/100-x
if the city could raise between $25 and $30 million for the purpose of removing the toxic pollutants, what is the range of pollutants that could be expected to be removed?
.05x/(100-x)=25 (in millions)
2500-25x = 0.05x
x= 2500/25.05 = 99.8%
Repeat same calculation for 30 millions.
To find the range of pollutants that could be expected to be removed, we need to evaluate the expression for different values of x within the given range.
The expression for the cost of removing x% of the toxic pollutants is:
Cost = 0.05x / (100 - x)
Now let's substitute different values of x within the given range of 25 to 30:
For x = 25:
Cost = 0.05(25) / (100 - 25) = 1.25 / 75 = 0.0167 million dollars
For x = 26:
Cost = 0.05(26) / (100 - 26) = 1.3 / 74 = 0.0176 million dollars
Continuing this process, we can find the cost for x = 27, 28, 29, and 30.
For x = 30:
Cost = 0.05(30) / (100 - 30) = 1.5 / 70 = 0.0214 million dollars
Now we have the cost of removing pollutants for each value of x. To find the range, we consider the minimum and maximum cost:
Minimum cost = cost for x = 25 = 0.0167 million dollars
Maximum cost = cost for x = 30 = 0.0214 million dollars
Therefore, the range of pollutants that could be expected to be removed is between 0.0167 million dollars and 0.0214 million dollars.