Math 103 Final Exam Review Practice Flashcards

A comprehensive set of vocabulary flashcards covering calculus, business math, algebra, and matrix applications for the Math 103 Final Exam.

Continuously Compounded Interest Formula

$A = Pe^{rt}$ where $A$ is the amount, $P$ is the principal, $r$ is the annual interest rate, and $t$ is the time in years.

Compound Interest Formula (m compounding periods)

$A = P \times (1 + \frac{r}{m})^{mt}$ where $m$ is the number of compounding periods per year.

Elasticity of Demand Function

$E(p) = -\frac{pf'(p)}{f(p)}$, used to measure the sensitivity of demand to changes in price.

Cash Flow Formula

$CF = P \times r$, representing the relationship between periodic payments, principal, and the rate of return.

Product Rule for Derivatives

$f'(x) = F'(x)S(x) + F(x)S'(x)$ where $F(x)$ is the first function and $S(x)$ is the second function.

Quotient Rule for Derivatives

$f'(x) = \frac{T'(x)B(x) - T(x)B'(x)}{(B(x))^2}$ where $T(x)$ is the top function and $B(x)$ is the bottom function.

Average Rate of Change

The ratio of the change in a function's value to the change in input across a specific interval, such as $\frac{f(x_2) - f(x_1)}{x_2 - x_1}$.

Linear Interpolation

A method used to estimate a value within two known data points by assuming a constant rate of change (a straight-line relationship).

Vertex of a Parabola

The highest or lowest point (maximum or minimum) of the graph of a quadratic function $f(x) = ax^2 + bx + c$.

Piecewise Function

A function defined by different formulas or rules for different parts of its domain.

Discontinuity

A target value on the x-axis where the graph of a function has a break, gap, or jump, causing the limit to perhaps not exist or not equal the function value.

Average Cost Function

Represented as ar{C}(x) = \frac{C(x)}{x}, it calculates the cost per unit produced at a production level of $x$.

Fixed Cost

The portion of the cost function that does not change with the number of units produced (represented by the constant term in a linear cost function).

Variable Cost

The cost that varies directly with the number of items produced (often the slope in a linear cost function).

Yield

The effective annual interest rate earned on an investment after accounting for the effects of compounding.

Present Value of a Perpetuity

The current value of a series of equal payments that continue forever, calculated using the relationship between the cash flow and the annual rate of return.

Marginal Revenue/Profit/Cost

The derivative of the function (e.g., $R'(x)$ or $P'(x)$) that estimates the change in the total for producing or selling one additional unit.

Break-even Point

The production level $x$ where total revenue equals total cost ($R(x) = C(x)$), resulting in a profit of zero.

Elastic Demand

A state where the elasticity of demand $E(p) > 1$, meaning demand is sensitive to price changes.

Inelastic Demand

A state where the elasticity of demand $E(p) < 1$, meaning demand is relatively insensitive to price changes.

Unitary Elasticity

A state where $E(p) = 1$, indicating that a percentage change in price results in an equal percentage change in demand.

Matrix Entry (i, j)

The specific element located in the $i$-th row and $j$-th column of a matrix.