Chapter 4.2, Problem 6E

Reminder Round all answers to two decimal places unless otherwise indicated.

Marriage Length 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 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 fifth.

a. What is the yearly decay factor for the exponential model?

b. Find an exponential model for M as a function of $n$.

c. According to your model, what fraction of women married for the first time in $1960$ celebrated their $40\text{th}$ anniversary? (Take $n=35$.) Round your answer to three decimal places. (The actual fraction is $0.449$ or $44.9\%$.)