Q$4.$

Data on biological oxygen demand versus time are modeled by the following equation

$y=k_1(1-e^{-k_{2}t})$

where $k_1$ is the ultimate carbonaceous oxygen demand $($mg$/1)$ and $k_2$ is the BOD reaction

rate constant $(d^{-1}).$ A set of BOD data were obtained and are given in the following table

$(1)$ Estimate the parameters $k_1$ and $k_2.$

$(2)$ Calculate the associated standard errors for $k_1$ and $k_2.$