# 010 Rates of Change - Chugging a Beer

## 2018/02/18

[latexpage]

### 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.

### More Beer Math

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