The median age for a first marriage in the United States for women was 25.9 in 2009 and 26.1 in 2010. Use an exponential model to predict the median age for women in 2019, where x is the number of years since 2009.

Question

eviant · Answer

@Zepdrix

Zepdrix · Answer

So if we let 2009 be our starting year,
$\large\rm f(x)=a\cdot b^x$
Then x=0 since 2009 to start,
(0, 25.9)

$\large\rm f(0)=25.9=a\cdot b^0$
So that gives us our a value, a=25.9

$\large\rm f(x)=25.9\cdot b^x$

Zepdrix · Answer

In 2010, our x will be 1,
(1, 26.1)

$\large\rm f(1)=26.1=25.9\cdot b^1$
So we can find our b value using some division,
$\large\rm b=\dfrac{26.1}{25.9}\approx 1.007722$

Zepdrix · Answer

$\large\rm f(x)=25.9(1.007722)^x$

Zepdrix · Answer

And then in 2019, our x will be 10,
$\large\rm f(10)=25.9(1.007722)^{10}$

Zepdrix · Answer

Let your calculator do the rest :D