The table provided shows the population of a town from 1996 to 2004, with the number of years $t$ since 1996 and the population $P$ in thousands.

Part a: Write the quadratic regression equation

From the question and the options, we are looking for a quadratic regression equation of the form: $f(t) = at^2 + bt + c$ where $t$ is the number of years since 1996.

The choices given are:

1. $f(t) = -0.213t^2 + 2.085t + 22.962$
2. $f(t) = -0.213t^2 + 2.084t + 22.963$

Part b: Predicting the population in 2007

The year 2007 is 11 years after 1996, so we substitute $t = 11$ into the chosen quadratic equation from part a.

We now need to identify which quadratic equation best fits the data and compute the population prediction for 2007 using the appropriate function.

Would you like me to walk through the regression calculation for the data or go directly to the solution using the choices provided?