Putting It Together

Most cities grow exponentially. You should know after completing this module that since populations are growing continuously as babies are born each day, a city’s population can be modeled by the equation: P = P0ert where P0 is your initial population of where you start measuring from, t is the time since your first measurement and r is the continuous growth rate. This is actually a fairly simple formula, but it has major implications. Let’s look at three cities whose original populations are measured in millions:

City Pop in 10 years Pop in 20 years Pop in 50 years
A P = 0.5e0.04t 0.746 1.113 3.694
B P = 0.8e−0.01t 0.724 0.655 0.485
C P = 1.5e0.01t 1.628 1.832 2.473
As a city planner, you can see how having an accurate model can help you predict city growth and better plan for the future.

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