Linear Population Growth

Do you know what the U.S. population is at this exact moment? The U.S. Census Bureau runs a virtualpopulation clockonline that shows an estimate of the U.S. population. This clock is an estimate based on three components: (1) the average frequency of births, (2) the average frequency of deaths, and (3) the average frequency of international net migration into the United States. Averaging these three variables will give the frequency of increase/decrease in population. (At the time this discussion was written, August 2014, the U.S. population will gain a person approximately every 12 seconds.) The three components to this model are reevaluated every month. This is obviously an estimate as one can recognize that the U.S. population varies nonlinearly throughout the month. You can generically model thistype oflinear population growthby an arithmetic sequence defined by the general term of:

P_n= P_(n-1)+ d where d is the average frequency of population increase (or decrease)

n = natural number indicating the nth growth period

P₀= initial population size

Initial Post:Create your own population growth model word problem for a classmate to solve.

1) Describe your population growth scenario in at least two paragraphs to give context for the math problem. For example, it could be the change in the prairie dog population each month in the open space across from your house or it could be the population size of infected people during the spread of an infectious disease.

2) Explicitly state your population growth model and include the following:

Initial population size, P₀

Population size after one growth period, P₁(i.e., days, months, or years)

Average change between growth periods, d

Growth model equation of the form P_n= P_(n-1)+ d