Continuous without restriction or Continuous with discrete interpretation I have a question , with contradictions with my teacher. Basically the question number is 7d .. And the instructions for number 7 questions are as follows:


  Determine whether each of the following function representation is
  discrete, continuous without restriction, or continuous with discrete
  interpretation.


And the graph for 7d question is:



The letter on top says Total Public expenditures since 1960. Ok so my teacher says its continuous with discrete interpretation while I say it's continuous. I say its continuous because dollars can be any point for example 12.5 billon dollars, 16.21313131 billon dollars, doesn’t matter. I don't understand why the teacher is saying continuous with discrete interpretation. Help Would be appreciated!

If you guys don't understand continuous with discrete interpretation , then my previous question explains it : 

https://math.stackexchange.com/questions/1929805/what-is-discrete-with-continuous-interpretation

If you guys don't know what continuous with no restriction means , it basically just means continuous
I want to extend my comment:

After reading the definitions in the referenced question I conclude that your teacher wants to say, that "continous with discrete interpretation" means, it makes only sense to speak about the public expenditures in 1961, 1962, 1963,.... So $f$ is only meaningful at 1,2,3,.. (years after 1960), and not e.g. at 1.2345 or at $\sqrt{2}$. But I am not sure if I am of the same opinion. Even if the data were supplied in a tabel (year, expenditures) I think one can speak about the expenditures a an arbitrary point in time. A more clear example is something like
$$f:A\to \mathbb{R}$$
$$f(x)=y$$
where $x$ is the number of inhabitants of a city and $f(y)$ are  the expenditures for public transport. Clearly there is no city with $1234567.8$ inhabitants, nevertheles it make sense to set $A=\mathbb{R^+}$ in a model with out any problems.
What makes your counterargument wrong in this case is simply the fact that money amounts always have a minimum possible value - in this case, pennies.  Any fractional amount of billions-of-dollars which specifies a fraction of a penny is simply not a real amount of money.  The curve in the diagram has to be a continuous curve interpolated through a discrete point-set of actual financial data.