The total cost of a sewage treatment plant with a capacity of $50$ million gallons per

day completed $2017$ for a new town in Colorado was $$4\mathrm{.}5$ million. It was proposed that a similar

treatment plant with a capacity of $80$ million gallons per day be built in another town in New Jersey

for completion in $2021.$ For additional information given below, make a screening estimate of the

cost of the proposed plant.

$$ In the total construction cost in Colorado, an item of $$300,000$ for site preparation is not

typical for similar plants.

$$ The variation of sizes for this type of treatment plants can be approximated by the

exponential law with m $=0\mathrm{.}5.$

$$ The inflation rate is approximately $5\%$ per year from $2015$ to $2025.$

$$ The locational indices of Colorado and New Jersey areas are $0\mathrm{.}95$ and $1\mathrm{.}10,$ respectively,

against the national average of $1\mathrm{.}00.$

$$ The installation of a special equipment to satisfy the new environmental standard cost an

extra $$200,000$ in $2021$ dollar for the New Jersey plant.

$$ The site condition in New Jersey required special foundation which cost $$500,000$ in $2021$

dollars.