(a) Call the number who married in 1960 = M
And.....5 years later......the number who remained married = .928M
And we have that one year later 98% of these remain married....so....... 0.98 (.928M) = .90944M
So
.90944M = .928M*e^(k * 1) divide by M
.90944 = .928*e^(k) divide by .928
.90944/.928 = e^(k) take the ln of both sides
ln (.90944/.928) = ln e^(k)
k = ln (.90944/.928) = -.02 = the decay factor
(b) The function is .928M * e^(-.02n) where n is the time in years since the 5th anniversary
(c) 45 years later we have
.928M * e ^(-.02 * 40) ≈ .417M [about 41.% remain married ]