The stream entering a $($completely mixed$)$ lake supplies the lake with a steady concentration of chemical B

after t$=0.$ In this lake, B biodegrades with a pseudo$-$first$-$order rate constant of k$.$

a$)$ Write the mass balance equation on B in the lake $($dB$/$dt$),$ and solve for the steady state concentration

within the lake, in terms of B o $,$ B in$,$ k$,$ Q$,$ and V$.$

b$)$ Write the Euler$$s method equation that could be used to solve for the non$-$steady state concentration of B

in terms of the same variables.

c$)$ Defining $95\%$ steady$-$state as: $0\mathrm{.}95=($B $$ B o $)/($B ss $$ B o $)$

Calculate the time it takes to reach $95\%$ steady$-$state in term of k$,$ V$,$ and Q $($or tau$)$ for the lake $.$