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

1. ### bigmac

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. ### HallsofIvy

40,785
Staff Emeritus
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.

3. ### LCKurtz

8,390
Perhaps you are supposed to find a best least squares fit to the data?