The median age for women in 2019 is 27.97.
What is median?
The median is the middle value when a data set is ordered from least to greatest. Median is a measure of central tendency which gives the value of the middle-most observation in the data.
For the given situation,
The median age for a first marriage in the United States for women in 2009 = 25.9 and
The median age for a first marriage in the United States for women in 2010 = 26.1
The above phenomenon can be modeled as
[tex]f(x)=a.b^{x}[/tex]
2009 is the initial year so x=0,
⇒ [tex]f(0)=ab^{0}[/tex]
⇒ [tex]25.9=a(1)[/tex]
⇒ [tex]a=25.9[/tex]
2010 is the next year so x=1,
⇒ [tex]f(1)=25.9(b)^{1} \\[/tex]
⇒ [tex]26.1=25.9b\\[/tex]
⇒ [tex]b=\frac{26.1}{25.9}[/tex]
⇒ [tex]b=1.007[/tex]
Thus for 2019, the number of years is 10.
The function becomes,
⇒ [tex]f(10)=25.9(1.007)^{10}[/tex]
⇒ [tex]f(10)=27.97[/tex]
Hence we can conclude that the median age for women in 2019 is 27.97.
Learn more about median here
https://brainly.com/question/21396105
#SPJ2
