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PreCalc Question

  1. Mar 28, 2010 #1
    1. The problem statement, all variables and given/known data

    The average growth rate of the population of a certain city is 7.5% per year. The city's population is now 22,750 people. What is the expected population in 10 years?

    2. Relevant equations

    I was always taught this formula for exponential growth

    N(t) = N_0 e^(kt)
    N = population
    N_0 = population at t(0)
    e = 2.7...
    k = some positive constant
    t = time

    Here's what my teacher wrote on my paper for the formula

    f(x) = C(1 + r)^x
    f(x) = population
    C = initial population
    r = growth rate

    3. The attempt at a solution

    no i dont understand how to do this exactly because I don't know what to use for the constant k

    so i used the second one

    22750 (1 + .075)^10 = 46888.4680

    now what I don't udnerstand is that this really makes no sense at all becasue if I wanted to fidn the population at 10 minutes or ten centuries and just plugged in 10 into the equation with no units at all I would get the same exact answer. Can youp please tell me how to go about reasoning this out... THANKS!
     
  2. jcsd
  3. Mar 28, 2010 #2

    Char. Limit

    User Avatar
    Gold Member

    The reason it works is because the growth rate must be defined using the inverse unit of whichever unit of time you're using.

    In this case, your growth rate is defined at 7.5% per year. If you used centuries for t, you'd have to find the growth rate per century.
     
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