These representations model a unique function and a particular set of circumstances. We might expect that similar circumstances would produce similar models. Each time we fill the tub some particulars might change – like how much water has collected when we start to count (t = 0) and how fast the water comes out of the faucet – but the general form of  V(t)  will probably remain unchanged.

We describe such collections of functions – generally the same but with a few well-defined differences – using parameters. Parameters are like little dials that we may adjust to tune a functional form to a particular set of circumstances.

Parameters for the bathtub might be:

• a  the initial volume of water in the tub at  t = 0  (in gallons);
  
  
• b  the rate at which water flows into the tub (in gallons/second).

The volume of water in the tub after  t  seconds could then be described by the equation:

V(t) = a + bt  gallons.

This equation, its table of values, and its graph would all change if we adjusted  a  and  b  to fit different circumstances. The general form of the representations, however, would be recognizably similar in every bathtub we filled.