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### The Beer Problem

I can chug a beer pretty fast. I recently timed myself drinking a full 12oz Beer (355mL) in just about 6 seconds. At what rate is the beer flowing down my throat?

### Slope

The slope formula, (m = \frac{rise}{run}), is a powerful tool for calculating and comparing steepness, or rates of changes. This is a very useful tool used in all aspects of engineering, mathematics, and even deep learning with neural networks.

#### Rate of Change

Did you know that the slope of a line is also referred to as the *rate* of change of the line?

Think about traveling on along a line on the x-y coordinate system. As you change from one position to the next, imagine time being passed in the horizontal direction and some other measurement being changed in the vertical direction. [m = \frac{Some Changing Quantity}{Amount Time Passed}]

#### Flow

In the case with beer, it’s the number of seconds passed along the horizontal and the amount of mili-liters changed during that time.

[m = \frac{Beer Changed}{Time Lapsed}]

The graphic depicted above starts off with a full beer (355mL). As time passes, due to a negative rate of change of volume (-mL/s e.g. chugging), notice it is empty around the 6 second mark.

A convenient shortcut used to denote a *change* in quantity is to use the Greek letter Delta, (\Delta).The slope equation now becomes, [m =\frac{\Delta mL}{\Delta t}; t > 0]

(t > 0) states that the line is not defined prior to (t = 0).

### Chug Video

This short video describes how rates of change of beer can be determined by examining the *slope*, or *rate of change*, of the line. The word *flow* means the rate at which volume changes per unit of time that passes.

[embed]https://youtu.be/P_dk7rCKlEQ[/embed]

### More Beer Math

For the previous beer related question, check this video out. Another one here.