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 40th anniversary? (Take
n = 35.) Round your answer to three decimal places.
ps. I saw that someone had this exact problem on here, I have parts a and c answered. I couldnt understand how they came up with part b though. I'm stressing right now. All of my college classes are online due to Covid-19 and I loathe online classes. Any help is appreciated.