To find: To model the given data with a fourth-degree polynomial.
The fourth-degree polynomial is .
The average age of first marriage of Japanese women has varied since 1950 is shown in table (1).
Model the given data with a fourth-degree polynomial.
Plot the graph between and using table (1) as shown in figure (1).
Refer the figure (1).
The fourth-degree polynomial for the curve is as below.
Equate the equation (1) with equation (2).
Compare the above equation.
, , , and .
To find: The model for by using part (a).
The value of is .
Calculate the value of .
Differentiate equation (1) with respect to .
Substitute for the expression , for the expression , for the expression and for the expression .
Thus, the value of is .
To estimate: The rate of change of marriage age for women in 1990.
The rate of change of marriage age for women in 1990 is .
Compute the rate of change of marriage age for women in 1990 using the formula below.
Substitute 1990 for t.
To sketch: The graph of data points and models for A and .
Plot the graph between and as shown in Figure (2).
Calculate the difference between the year 1950 and 1955.
Substitute the value 5 for the expression in the equation (2).
Similarly, calculate the value of for the following values of in table (1).
Tabulate the value of as shown in table (2).
Plot the graph between and using the table (2) as shown in Figure (3).
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