Period=1; (* year *)
k=2Pi/Period;
Amplitude = 3 ;(* ppm *)
PhaseShift=0 ;(* looks like a sine wave starting from the beginning of the year, so if we treat January as x=0, we're good. *)
Oscillation[x_]:=Amplitude*Sin[k*x]
Plot[Oscillation[x],{x,0, 1}]

CO21960=316;
CO21990=353;
CO22010=384;
(* we'll use two of these data points to create a linear model for the trend: *)
m=(CO22010-CO21960)/(2010-1960)
LinearFit[x_]:=m*(x-1960)+CO21960
Model[x_]:=LinearFit[x]+Oscillation[x]
Plot[Model[x],{x,1960,2010},PlotPoints->1000]

(* Now we'll predict the future: what will the value of CO2 be in the period leading up to 2050?

Notice the funny gaps in the oscillation in this next plot -- because we're not using enough points in the plot, as I did above: *)
Plot[Model[x],{x,1960,2050}]
(* let's make sure that there are enough points: *)
Plot[Model[x],{x,1960,2050},PlotPoints->1000]