\(
Clear[k, a, kmax, kn, f, V, \ q, \ \ P, \ Q, \ ode1, ode2, 
      maxtime]
\)
a = 0.5;
kmax = 2.0;
kn = 0.75;
f = 1.0;
V = 1.0;
q = 1.0;
\(\(maxtime = 100;\)
	\)
\(	ode1 = \ \(P'\)[t] == 
        P[t] \((\(kmax\ Q[t]\)\/\(kn\  + \ Q[t]\))\)\  - \(\(\ \)\(f\ P[t]\)\)\/V\)
\(ode2 = \ \(Q'\)[
          t]\  == \(-a\)\ P[
              t] \((\(kmax\ Q[t]\)\/\(kn\  + \ Q[t]\))\)\  - \(\(\ \)\(f\ Q[t]\)\)\/V\  + \(\(\ \)\(f\ q\)\)\/\(\(V\)\(
\)
            \)\)

sol = 
        NDSolve[{ode1,  ode2,  P[0. ] == 1.25,  Q[0. ] == 1.25},  {P[t], 
            Q[t]},  {t, 0, maxtime}];

\(\(\(
\)\(p1 = 
      Plot[Evaluate[{P[t]} /. sol], \ {t, 0, 
          maxtime}, 
		\ PlotStyle -> {RGBColor[1, 0, 
              0]}, 
		PlotLabel -> "BACTERIAL POPULATION"]\)\)\)

\(\(\(
\)\(p2 = 
      Plot[Evaluate[{Q[t]} /. sol], \ {t, 0, 
          maxtime}, 
		PlotRange -> {0, 1}, \ 
        PlotStyle -> {RGBColor[1, 0, 
              0]}, 
		PlotLabel -> "NUTRIENTS"]\)\)\)

q3 = P[t] /. sol[[1]]
q4 = Q[t] /. sol[[1]]
phaseplot2 = ParametricPlot[{q3, q4}, {t, 0, maxtime}]