Answer
a) The model is found to be $y=0.00452 t^2+0.265 t + 2.74.$.
b) The graph is on the figure along with the points of original data. The data agrees well with the model.
c) The predicted GDP in $2020$ is $y=20.57$
Work Step by Step
a) You can use Wolfram Mathematica to find the regression coefficients $a$, $b$ and $c$ for the model. Using the command
"FindFit[Data, {a t^2 + b t + c}, {a, b, c}, t]" we find
$$a=0.00452;\quad b=0.265;\quad c=2.74$$
so we can write
$$y=0.00452 t^2+0.265 t + 2.74.$$
b) The graph is shown on the figure, along with the points from the table in the problem. We see that the points agree well with the model.
c) To predict this firs notice that if $1980$ corresponds to $t=0$ then $2020$ corresponds to $t=40$. Now just calculate $y$ from the model to obtain the predicted GDP:
$$y=0.00452\times40^2 + 0.265\times 40 + 2.74 = 20.57$$ which is the required value.
