$5\mathrm{.}5$ Mathematical models are used to predict the growth of a population, that is$,$ population size at some future date. The simplest model is that for exponential growth. The calculation requires knowledge of the organism's maximum specific growth rate. A value for this coefficient can be obtained from field observations of population size or from laboratory experiments where population size is monitored as a function of time when growing at high substrate concentrations $(S{K}_s)($Table $5\mathrm{.}16)$:

$\backslash$table$[[\backslash$table$[[$Field Observations of Population Size$],[$Over Time$]]],[$Time $($days$),$Biomass $($mg$/$L$)],[0,50],[1,136],[2,369],[3,1,004],[4,2,730],[5,7,421]]$

Calculate ${}_{\text{m}\text{a}\text{x}}$ for this population, assuming exponential growth; include appropriate units.