The following table gives the U.S. population, ages 20–64, (in millions) for selected years from 1950 and projected to 2050. Year Millions Year Millions 1950 92.8 2010 189.1 1960 99.8 2020 198.2 1970 113.0 2030 202.8 1980 134.0 2040 213.3 1990 152.7 2050 224.3 2000 169.8 (a) Find the logistic function that models these data. Use x as the number of years after 1950 and report your model with 3 significant digit coefficients. y = 251(1+2.56e(−0.0273x)) (b) Use the unrounded model to predict the U.S. population (in millions) ages 20–64 in 2005. (Round your answer to one decimal place.) million (c) What year does the unrounded model predict this group's population will reach 200 million?
The following table gives the U.S. population, ages 20–64, (in millions) for selected years from 1950 and projected to 2050. Year Millions Year Millions 1950 92.8 2010 189.1 1960 99.8 2020 198.2 1970 113.0 2030 202.8 1980 134.0 2040 213.3 1990 152.7 2050 224.3 2000 169.8 (a) Find the logistic function that models these data. Use x as the number of years after 1950 and report your model with 3 significant digit coefficients. y = 251(1+2.56e(−0.0273x)) (b) Use the unrounded model to predict the U.S. population (in millions) ages 20–64 in 2005. (Round your answer to one decimal place.) million (c) What year does the unrounded model predict this group's population will reach 200 million?
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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The following table gives the U.S. population, ages 20–64, (in millions) for selected years from 1950 and projected to 2050.
| Year | Millions | Year | Millions |
|---|---|---|---|
| 1950 | 92.8 | 2010 | 189.1 |
| 1960 | 99.8 | 2020 | 198.2 |
| 1970 | 113.0 | 2030 | 202.8 |
| 1980 | 134.0 | 2040 | 213.3 |
| 1990 | 152.7 | 2050 | 224.3 |
| 2000 | 169.8 |
(a)
Find the logistic function that models these data. Use x as the number of years after 1950 and report your model with 3 significant digit coefficients.
y =
251(1+2.56e(−0.0273x))
(b)
Use the unrounded model to predict the U.S. population (in millions) ages 20–64 in 2005. (Round your answer to one decimal place.)
million
(c)
What year does the unrounded model predict this group's population will reach 200 million?
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