AP Precalculus Unit 2 Notes: Understanding Exponentials Through Patterns, Graphs, and Models (copy)

sequence

An ordered list of numbers called terms that follow a specific rule.

arithmetic sequence

A sequence that changes by adding or subtracting the same number each step.

common difference

The constant amount added or subtracted in an arithmetic sequence.

geometric sequence

A sequence that changes by multiplying by the same number each step.

common ratio

The constant factor by which terms are multiplied in a geometric sequence.

exponential function

A function where the input appears in the exponent, typically in the form f(x)=ab^x.

initial value

The value of the function at x=0, represented by a in exponential functions.

exponential growth

The increase of a quantity by a constant percentage per unit of time.

exponential decay

The decrease of a quantity by a constant percentage per unit of time.

doubling time

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

half-life

The amount of time required for a quantity to reduce to half its initial amount.

residual

The difference between the observed value and the predicted value in a model.

linear model

A model that describes a relationship with constant additive change.

exponential model

A model that describes a relationship with constant multiplicative change.

typical question patterns

Common types of questions on tests, such as identifying sequences or writing models.

common mistakes

Frequent errors that students make, such as using the wrong type of change for models.