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Write an exponential equation from this data (data table included) 
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#1
Jun1310, 12:33 PM

P: 16

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
Jun1310, 03:58 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,565

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. 


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