QuestionShown to the right is a certain population, in billions, for seven selected years from 1950 through 2006. Using a graphing utility's logistic regression option, we obtain the logistic growth model shown below for population, $\mathrm{f}(\mathrm{x})$, in billions, x years after 1949. How well does the function model the data for 2006? $$f(x)=\frac{11.82}{1+3.81 e^{-0.027 x}}$$ \begin{tabular}{|c|c|} \hline X, Number of Years after 1949 & y, Population (billions) \\ \hline $1(1950)$ & 2.6 \\ \hline $11(1960)$ & 3.0 \\ \hline $21(1970)$ & 3.7 \\ \hline $31(1980)$ & 4.5 \\ \hline $41(1990)$ & 5.3 \\ \hline $51(2000)$ & 6.1 \\ \hline $57(2006)$ & 6.5 \\ \hline \end{tabular}
For 2006 , the function $\square$ the population to one decimal place. accurately predictś slightly underestimates slightly overestimates