LESSON 2 VIDEO 3 Business Mathematics and Linear Equations Flashcards

This set of vocabulary flashcards covers essential business terms, breakeven analysis, interest calculations, and linear population modeling based on the lecture transcript.

Break-even

A state in business where the money being spent (costs) and the money being brought in (revenue) are equal, resulting in no loss and no profit ($\text{Profit} = 0$).

Revenue

The total money coming into a business.

Cost

The total money going out of a business.

Profit Formula

The mathematical expression defined as $\text{Profit} = ext{Revenue} - ext{Cost}$.

Thumb Drive Break-even Point

The production level for a manufacturer where total cost is $2x + 7,920$ and total revenue is $20x$, calculated at $x = 440$ thumb drives.

Satellite System Break-even Point

The number of systems needed to be sold to reach zero profit ($p = 0$) given the function $4p = 81x - 29,970$, which is $370$ systems.

Credit Card Interest Equation

An approximation formula for interest paid ($I$) on a \text{$10,000} debt over three years at $r$ percent: $\frac{I}{175.393} + 0.663 = r$.

$$3,356.50$$

The amount of interest paid over three years on a \text{$10,000} credit card debt with an interest rate of $19.8\%$, rounded to the nearest cent.

UK Population Approximation Equation

A linear equation where $y$ is the population in millions and $x$ is the number of years after 2000: $10y - 4.55x = 581$.

$x$ (in UK Population Model)

The variable representing the number of years after 2000; for example, in the year 2022, $x = 22$.

$y$ (in UK Population Model)

The variable representing the population of The United Kingdom in millions of people.

2030

The projected year when the population of The United Kingdom will reach $71,750,000$ (or $y = 71.75$), calculated based on $x = 30$.