MATH1044 Chapter Review Flashcards

Vocabulary flashcards covering key definitions, formulas, and concepts from the MATH1044 review problems.

Definition of Continuity at $x = a$

A mathematical condition requiring three parts: 1) $\lim_{x \to a} f(x)$ exists, 2) $f(a)$ exists, and 3) $\lim_{x \to a} f(x) = f(a)$.

Percent Change Formula

The formula used to measure relative change: $\% \,\text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\%$.

Units of Slope

The units defining a rate of change, calculated as $\frac{\text{units of output}}{\text{units of input}}$.

Break-even Point

The production level $q$ where total revenue equals total cost, represented as $R(q) = C(q)$.

Compound Interest Formula

The formula for periodic compounding interest: $F = P \left(1 + \frac{r}{n}\right)^{nt}$, where $P$ is principal, $r$ is annual rate, $n$ is compounding frequency, and $t$ is time.

Continuous Compound Interest Formula

The formula for continuously compounded interest: $F = P e^{rt}$, where $P$ is principal, $r$ is annual rate, and $t$ is time.

Annual Percentage Yield (APY) Formula

The effective annual rate of return: $\text{APY} = \left(1 + \frac{r}{n}\right)^n - 1$, where $r$ is nominal interest rate and $n$ is compounding periods per year.

Average Cost Function

The cost per unit for producing $q$ items, calculated by dividing the cost function by quantity: $\frac{C(q)}{q}$.

Profit Function

The total financial return calculated as revenue minus cost: $P(q) = R(q) - C(q)$.

Inverse of an Exponential Function

A logarithmic model obtained by swapping the input variable $x$ and output variable $y$.

Half-life

The amount of time it takes for a decaying quantity to reduce to half of its initial amount.

Doubling Time

The period of time required for a growing population or quantity to double in size.