Most valuable coefficient

Algebra Level 5

\[\begin{eqnarray} f(15) &=& 125 \\ f(16) &=& 150 \\ f(17) &=& 210 \\ f(18) &=& 275 \\ f(19) &=& 365 \\ \end{eqnarray} \]

Let \(f(x) \) denote the a \(5^\text{th} \) degree polynomial with leading coefficient 3 such that it satisfies all the equations above. Find the value of \(f(20) \).

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