Wildlife,
A wildlife management team studied the reproductive rates of deer in four tracts of a wildlife preserve. In each tract, the number of females $x$ and the percent of females $y$ that had offspring the following year were recorded. The table shows the results.
$$
\begin{array}{|l|c|c|c|c|}
\hline \text { Number, } x & 100 & 120 & 140 & 160 \\
\hline \text { Percent, } y & 75 & 68 & 55 & 30 \\
\hline
\end{array}
$$
(a) Find the least squares regression parabola $y=a x^2+b x+c$ for the data by solving the system.
$$
\begin{aligned}
4 c+520 b+69,600 a & =228 \\
520 c+69,600 b+9,568,000 a & =28,160 \\
69,600 c+9,568,000 b+1,346,880,000 a & =3,575,200
\end{aligned}
$$
(b) Use a graphing utility to graph the model you found in part (a) and the data in the same viewing window. How well does the model fit the data? Explain.
(c) Use the model to estimate the percent of females that had offspring when there were 170 females.
(d) Use the model to estimate the number of females when $40 \%$ of the females had offspring.