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Question 947586: According to the National Center for Health Statistics, in 1990, 28% of babies in the United States were born to parents who were not married. Throughout the 1990s, this increased by approximately 0.6% per year. If this trend continues, in which year will 76% of babies be born out of wedlock?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! start with 28%.
each year that percentage increases by .6%.
you will multiply 28% by 1.006 every year until it reaches 76%.
the formula for that is fv = pv * (1+i)^n
fv is the future value which will be 76%.
pv is the present value which is 28%.
i is the interest rate per time period which is equal to .6% / 100 = .006
n is the number of time periods.
since we are dealing with an increase per year, the time period is measured in years.
the formula becomes:
76 = 28 * 1.006^n
we don't know what n is so we have to solve for it.
divide both sides of this equation by 28 to get:
76/28 = 1.006^n
take the log of both sides of this equation to get:
log(76/28) = log(1.006^n)
since log(1.006^n) is equivalent to n * log(1.006), the equation becomes:
log(76/28) = n * log(1.006)
divide both sides of this equation by log(1.006) to get:
log(76/28) / log(1.006) = n
solve for n to get:
n = 166.9202383
it would take 166.9202383 years for the percent of babies to be born out of wedlock to reach 76 percent if the rate of increase in the percent was 0.6% per year.
since you started in 1990, then 166.9202383 years after that would be in the year 1990 + 166 = some time in the year 2156.
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