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Calculating Exponential function

Hello, I am really struggling on question #23. I can't seem to find the appropriate Exponential Function that best fits this data.

The general formula is f(x) = a * b ^ x , where a is the first term, b is a the growth factor and x is the variable.

Let x represent time after 1950.

If a = 132 459

f(x) = 253 539

x = 20? //This part I am not sure about

So my attempt would look like this:

253 539 = 132 459 ( b ) ^ 20

b = 1.03299

However, f(x) = 132 459 ( 1.03299 ) does not satisfy the year at 1994, x = 44.

Attachment 30019

Where did I go wrong?

Re: Calculating Exponential function

Hey sakonpure6.

You have to use the average rate of growth and not any specific value. It's not expected that you will have an exponential curve that passes through all points.