Mathematical
Modeling
Math 485/585
Modeling the growth of the U.S. population
Modeling global population changes
- We will use data provided by the U.S. Census Bureau.
The folowing
link contains population estimates between 1900 and 2000. You can download the
corresponding file by right-clicking on this link. Population estimates between
two censuses are obtained as described in the
methodology for
post 2000-Census estimates.
- Import this data into Excel and plot the U.S. population as a function of time. What
do you conclude ?
- Can the growth of the U.S. population be modeled by a simple evolution equation of
the form N(t+1) = (1+R) N(t), where t is in years?
Why or why not ?
If so, find R.
Model with different age groups
- The following link contains
population estimates by five-year age groups from 1989 to 1999.
- Use this information to plot the age distribution in the U.S. for different years.
- Has there been major changes in the last 10 years ?
- The data has 21 age groups. Use the age distribution to define larger age groups
that can be used in a simplified model.
- The National Center for Health Statistics can
provide data on birth and death rates. You may want to use the links below to estimate
the birth rates from 1989 to 1998 as well as death rates per age groups.
- Use the above data to predict the population of the various age groups in 1998,
given the population in each age group in 1989.
How does your model compare to the actual data for 1998 ?
Use your model to predict the population in each age group in 2025. What do you conclude ?