Answer:
76 % of babies will be born out of wedlock in the [tex]81^{st}[/tex] year
Step-by-step explanation:
Given: In 1990, 28 % of babies in the United States were born to parents who were not married. This increased by approximately 0.6 % per year.
To find: year when 76 % of babies born out of wedlock
Solution:
A sequence is said to be in arithmetic progression if the difference between the terms is same.
For a sequence with first term as 'a' and common difference as 'd', the nth term is given by [tex]a_n=a+(n-1)d[/tex]
The given situation also forms an arithmetic progression with [tex]a=28\,,\,d=0.6[/tex]
Also, put [tex]a_n=76[/tex]
So,
[tex]a_n=a+(n-1)d\\76=28+(n-1)(0.6)\\76-28=0.6(n-1)\\48=0.6(n-1)\\\frac{48}{0.6}=n-1\\\\80=n-1\\n=80+1\\n=81[/tex]
So, 76 % of babies will be born out of wedlock in the [tex]81^{st}[/tex] year
