It is awkward mostly because your notation is not useful. Have you never seen simple function notation?

I believe you might mean this:

"I have a curve that is +21 on the X, +9 on the Y"

f(21) = 9

"assuming your starting at 0/0 for the first point"

f(0) = 0

"At 14x, Y=3.11."

f(14) = 3.11

"At 7x, Y=.51."

f(7) = 0.51

This gives four points: (0,0),(7,0.51),(14,3.11),(21,9)

Please observe these substantially more compact and useful notational conventions.

Now you must decide...

Why do you think an exponential model would be good?

Are you SURE you want it to go through (0,0)?