Write an exponential equation from this data (data table included)

  1. 1. The problem statement, all variables and given/known data
    - The following table gives the population of a city over time:

    2. Relevant equations

    I know this equation: y = a(b)x

    and exponential growth: b = 1 + growth rate and b = 1 - decay rate

    3. The attempt at a solution

    I know from back in chapter 2 that first differences = linear model, second differences are the same = quadratic and if the 3rd differences are the same then its a cubic model...but that doesn't work here. I am completely stuck....how do I find the model. Any hints/tips/methods will be greatly appreciated!! Thanks!!
  2. jcsd
  3. HallsofIvy

    HallsofIvy 41,260
    Staff Emeritus
    Science Advisor

    There are two unknown constants in your formula, a and b. You need two equations to solve for two unknowns so pick two points (typically, it is best to endpoints, here 1954 and 1994).

    That will give you [tex]132459= ab^{1954}[/tex] and [tex]514013= ab^{1994}[/tex]

    It should be easy to see that dividing one equation by the other will eliminate a, leaving a single equation to solve for b.
  4. LCKurtz

    LCKurtz 8,448
    Homework Helper
    Gold Member

    Perhaps you are supposed to find a best least squares fit to the data?
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