Question

2 A short-term economic model assumes that a country's GDP $G$ (in 100 billion Euro) at time
$t$ (in years) can be expressed as a quadratic polynomial $G(t) = At^2 + Bt + C$.
Initially $G$ has a value of $20$. At $1$ year the value of $G$ is $20.5$ and at $2$ years the value
of $G$ is $21$.

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Determine the values of the constants $A, B, C$. Is the value of $B$ equal to:

\begin{enumerate}
\item[(a)] $0$,

\item[(b)] $0.5$,

\item[(c)] $1$,

\item[(d)] none of the above?
\end{enumerate}

Answer 1

$G(t)=At^2+Bt+C\\At\ t=0\\G(t)=20\\so\\C=20\\At\ t =1\\G(t)=20.5\\so\\20.5=A+B+C\\or\\A+B=0.5\ \ \ ........(1)\\At\ t\ =2\\G(t)=21\\so,\\21=4A+2B+C\\or \\4A+2B=1\ \ \ \ ........(2)\\on\ taking\ (1)\ and\ (2)\\2A+2B=1\ \ \ \ ..........(3)\\on\ subtracting\ equation\ (3)\ from\ (2)\ we\ get\\2A=0\ or\ A=0\\putting\ the\ value\ of\ A\ in\ equation\ (1)\ we\ get\ B=0.5\\ we\ get,\\A=0\\B=0.5\\C=20\\so\\value\ of\ B\ equals \ (b)=0.5$