How do i use a regression to represent the growth exponentially?

Question

using the data for SAN DIEGO CITY only.

heres the link: http://www.sandiegohistory.org/links/sandiegopopulation.htm

Answer 1

u have to fit an exponential model to the data.ud know what im talking about if u study studied about fitting an exponential model(usually least squares) of the form y=ae^bx.u can either use ur calculator to fingd the parameters(a and b) or http://www.xuru.org/rt/ExpR.asp

Answer 2

Exponential growth follows the equation Y = A*B^x
Ln(Y) = ln(A) + x*ln(B)
Let y = Ln(Y)
a = ln(A)
b = ln(B)
Then
y = a + bx
which is the equation used for straight-line regression.
Note that x is unchanged in the substitution.
Now you run your regression on ln(F) vs x, yielding constants a and b
Inverting the transformation, you have
A = e^a
B = e^b

The other exponential form you can use this type of transform on is
y = Ae^Bx
ln(Y) = ln(A) + Bx
Running the same straight-line regression will yield a and B. With this form you only exponentiate a (A = e^a) since B = b. B becomes the coefficient of x in the exponent of e.

In either case, your solution matrix will be
| n . .. ∑x | | a | | ∑ln(F) . |
| ∑x ∑x^2 | | b | | ∑xln(F) |