Two young mathematicians think about the plots of functions.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Riley, remember when I asked you about compound interest?
Riley
Yes I do! You were dealing with a formula like
Devyn
I was. With monthly compoundings and 3% interest with a principal of $1, it became just
Riley
I remember that. What about it?
Devyn
As time passes, the account is worth more and more.
Riley
Makes sense. You are gaining interest each month.
Devyn
But by how much? How fast is it growing?
Riley
You are thinking about rates of change!
Devyn
Right! How do we find the derivative ?
Riley
It isn’t a polynomial, so we can’t use Power Rule. What can we do?
What is the AVERAGE rate of change of over the first 2 years (so from to )? (ROUND TO 2 DECIMAL PLACES)
. . . .
What are the units of that average rate of change?
dollars years dollars/year years/dollar It does not have a unit