How do I determine if graph is supposed to be discrete or continuous?

Question

I am working on exponential functions in algebra right now and my teacher has given me word problems and then has asked me to find the best graphical problem I can create based on the context. My teacher wants us to figure out of the relationship is linear or exponential ( I already understand this) and then if the context is best modeled as a discrete or continuous function. This is the part I am struggling with and do not understand. All I really know is that a discrete graph has scatter plots and a continuous function is connected with a line. I'm unsure how to know which one it is as I'm creating the graphs. I just need a good description of how to tell the difference and a few examples, please. Thank you.

Answer 1

Discrete means separate points that you cannot break into "in between" points.

Example: There are 36 students how must ride the school bus. Each bus holds 24 students. How many buses must be used. The answer, of course is 2 buses because buses are discrete. If the function were continuous, then we could say it takes 1.5 buses but there is no such thing as half a bus (at least it couldn't be driven to school.

Other examples of discrete functions:

It costs $10 per movie ticket. You have $32. How many people get to see the movie? If continuous, it would be 3.2 people. But it is not possible to take 0.2 people to the movie. The number of people is discrete meaning you bring 1, 2, 3, 4, etc to the movies.

Soda is on sale for $2 for a 2 liter bottle but that is the only size they have available. Although the unit cost $1 per liter, it is not possible to purchase soda in any other increment than 2 liter bottles. So you can spend $2 and get 2 liters, $4 and get 4 liters, etc, but you cannot pay $3.82 to purchase 3.82 liters.

The height of basketball players is roughly linear to their shoe size. Despite the fact that you can measure a basketball players height to very small units (essentially continuous, just requiring better and better measuring equipment), shoe size is available (in the US) in 1/2 sizes (size 10, 10 1/2, 11, 11 1/2, 12, etc). Shoe size is discrete.

Example of continuous functions:

The temperature will increase by 1 degree per hour this morning until noon. It is currently 60 degrees. How many hours go by until it is 64.652 degrees? Obviously, 4.652 hours, right? This function is continuous because you can break down both temperature and time into the finest increments that you can measure. And when you get down to 3 decimal points, you can get better equipment and measure down to 4 decimal points, etc, etc.