n this exercise, we consider data from the Statistical Abstract of the United States on the fraction of women married for the first time in 1960 whose marriage reached a given anniversary number. The data show that the fraction of women who reached their fifth anniversary was 0.928. After that, for each one-year increase in the anniversary number, the fraction reaching that number drops by about 2%. These data describe constant percentage change, so it is reasonable to model the fraction M as an exponential function of the number n of anniversaries since the fifth. (a) What is the yearly decay factor for the exponential model?

In this exercise, we consider data from the Statistical Abstract of the United States on the fraction of women married for the first time in 1960 whose marriage reached a given anniversary number. The data show that the fraction of women who reached their fifth anniversary was 0.928. After that, for each one-year increase in the anniversary number, the fraction reaching that number drops by about 2%. These data describe constant percentage change, so it is reasonable to model the fraction M as an exponential function of the number n of anniversaries since the fifth.

(a) What is the yearly decay factor for the exponential model?
  

(b) Find an exponential model for M as a function of n. (Let 

n = 0

 represent the fifth anniversary.)

M = 

 

 

 

(c) According to your model, what fraction of women married for the first time in 1960 celebrated their 35th anniversary? (Take 

n = 30.)

 Round your answer to three decimal places.

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