A contaminated soil from an industrial site is to be decontaminated in an aerated lagoon.

To determine the time required to treat the contaminated soil, a laboratory scale completely mixed

batch reactor is used to generate the following data.

Time $($d$)$ Waste concentration $($mg$/$L$)$

$4300$

$5270$

$7210$

$15100$

Assuming $1$st order kinetics for decay, estimate the decay rate constant. Given the lab technician did

not measure the waste concentration for the first $3$ days of the lab test, you must also make an

estimate of the initial concentration of the waste. The utility operating the aerated lagoon has asked

you to make estimates of the time required for $90,99$ and $99\mathrm{.}5\%$ reductions in the concentration of

the waste. You must also determine whether any of these conditions are likely to meet the target of

less than $1$ ppm of contamination, upon which the treated waste may be easily disposed of