$2\mathrm{.}5)$ The following data is available from a bioreactor where succinate, a food additive, is produced by a microorganism from glucose. Citrate concentration is measured in the bioreactor over time:

You would like to apply a black$-$box modeling approach to the data, and fit it to the following model $C=(k_1{t}^2+k_2{)}^2$ with $k_1$ and $k_2$ are model parameters.

$($a$)$ Apply a transformation to the data to make it solvable on pen$-$and$-$paper.

$($b$)$ Write the error function and derive the equations for the identification of the parameters.

$($c$)$ Solve the resulting linear systems of equations using the data to identify the parameters.

$($d$)$ If you are asked to not to perform any transformation but follow nonlinear modeling, what would be the resulting $F$ and $G$ functions for the identification of the parameters? Derive the equations.