data={{.5,11.4},{6,9.936`},{12,9.571`},{18,9.754`},{24,9.439`},{30,9.431`},{36,9.43`},{42,8.954`},{48,9.542`}}

Every day for 2 weeks

Manipulate[f[x_]:=d+k x;ListPlot[Table[{t,Nest[f,0,t]},{t,0,time}],PlotRange->{{0,14},{0,1}},PlotStyle->{PointSize[.02],Black},Frame->True,FrameLabel->{"Day, n","(Subscript[C, n])"},LabelStyle->Directive[FontSize->14],PlotStyle->{Black}],{time,1,14,1},{{d,0.2},0.1,.4,Appearance->"Labeled"},{{k,0.3},.1,.6,Appearance->"Labeled"}]

f[x_]:=x+a-k x

a=2;k=.01;

NestList[f,11.45,15]

10/1

Eveey six hours for (start at 5.5 and 0.6)

Manipulate[data={{.5,11.4},{6,9.936`},{12,9.571`},{18,9.754`},{24,9.439`},{30,9.431`},{36,9.43`},{42,8.954`},{48,9.542`}};f[x_]:=d+k x;ListPlot[{data,Table[{6 t,Nest[f,11.45,t]},{t,0,time}]},PlotRange->{{0,50},{5,12}},PlotStyle->{{PointSize[.02],Blue},{PointSize[.02],Black}},Frame->True,FrameLabel->{"Hour, n","(Subscript[C, n])"},LabelStyle->Directive[FontSize->14],PlotStyle->{Black}],{{time,8},0,8,1},{{d,5.5,d},4,6,Appearance->"Labeled"},{{k,0.4},.3,.5,Appearance->"Labeled"}]