Question

The table shows how the average age of first marriage of Japanese women has varied since $1950 .$ $$\begin{array}{|c|c||c|c|}\hline t & {A(t)} & {t} & {A(t)} \\ \hline 1950 & {23.0} & {1985} & {25.5} \\ {1955} & {23.8} & {1990} & {25.9} \\ {1960} & {24.4} & {1995} & {26.3} \\ {1965} & {24.5} & {2000} & {27.0} \\ {1970} & {24.2} & {2005} & {28.0} \\ {1975} & {24.7} & {2010} & {28.8} \\ {1980} & {25.2} & {} \\ \hline\end{array}$$ (a) Use a graphing calculator or computer to model these data with a fourth-degree polynomial. (b) Use part (a) to find a model for $A^{\prime}(t) .$ (c) Estimate the rate of change of marriage age for women in 1990 . (d) Graph the data points and the models for $A$ and $A^{\prime}$.

          The table shows how the average age of first marriage of Japanese women has varied since $1950 .$
$$\begin{array}{|c|c||c|c|}\hline t & {A(t)} & {t} & {A(t)} \\ \hline 1950 & {23.0} & {1985} & {25.5} \\ {1955} & {23.8} & {1990} & {25.9} \\ {1960} & {24.4} & {1995} & {26.3} \\ {1965} & {24.5} & {2000} & {27.0} \\ {1970} & {24.2} & {2005} & {28.0} \\ {1975} & {24.7} & {2010} & {28.8} \\ {1980} & {25.2} & {} \\ \hline\end{array}$$
(a) Use a graphing calculator or computer to model these data with a fourth-degree polynomial.
(b) Use part (a) to find a model for $A^{\prime}(t) .$
(c) Estimate the rate of change of marriage age for women in 1990 .
(d) Graph the data points and the models for $A$ and $A^{\prime}$.

Added by Juan C.

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