In time-series analysis, one approach to modeling trends in data involves the use of a trend-line regression. A common method to capture trends is the linear trend model, which can be represented by the equation:

$$ Y_t = eta_0 + eta_1 t + eta_2 t^2 + ext{error} $$

where:

• $$ Y_t $$ is the value at time $$ t $$,
• $$ eta_0 $$ is the intercept,
• $$ eta_1 $$ is the coefficient for the linear term,
• $$ eta_2 $$ is the coefficient for the quadratic term.

After estimating the coefficients using ordinary least squares, the analysis reveals that $$ eta_0 = 5 $$, $$ eta_1 = 2 $$, and $$ eta_2 = 0.5 $$. What is the predicted value of $$ Y $$ for $$ t = 4 $$?