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 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 exponenti 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 1960 celebrated their 40th anniversary? (Take n = 35.) Round your answer to three decimal places.
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 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 exponenti 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 1960 celebrated their 40th anniversary? (Take n = 35.) Round your answer to three decimal places.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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.
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