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

[bigmac]

Homework Statement

- The following table gives the population of a city over time:

Homework Equations

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

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

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!

 

[HallsofIvy]

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 $$132459= ab^{1954}$$ and $$514013= ab^{1994}$$

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

 

[LCKurtz]

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