Question

Which of the following are continuous functions of time?

The quantity of gas in the tank of a car on a journey between New York and Boston (continuous or discontinuous)
The number of students enrolled in a class during a semester (continuous or discontinuous)

I want to verify my answers:
Discontinuous for the car
Continuous for the students,

Answer 1

The quantity of gas in a car's tank during a journey is continuous, whereas the number of students enrolled in a class is discontinuous due to discrete changes.

Step-by-step explanation:

Continuous functions of time imply that values can change smoothly without jumps or breaks. For the quantity of gas in the tank of a car on a journey between New York and Boston, this would be a continuous function because the gas level decreases gradually as the car is driven. However, for the number of students enrolled in a class during a semester, this is a discontinuous function, because the enrollment can only change through discrete additions or subtractions when students enroll or drop out of the class.

Answer 2

Continuous functions of time are a function if small changes are made to the source then the result will have those small changes in them. The quantity of gas is a continuous function of time because small variations can be made to the quantity of the gas in use to the extent of molecules and atoms whereas same cannot be done to the student as we cannot half them.