AP Precalculus: Unit 2A; 2.5.A Exponential Context and Data Modeling

These flashcards cover key concepts and terms related to exponential and logarithmic functions from the lecture notes.

Exponential Functions

Functions that model growth patterns where successive output values over equal-length input-value intervals are proportional.

Proportional Growth Pattern

A situation where the output values increase or decrease in proportion to their input values, often modeled by exponential functions. A constant may need to be added to the dependent variable values of a data set to reveal a proportional growth pattern.

Natural Base (e)

The constant approximately equal to 2.718, often used as the base in exponential functions.

Growth Factor (b)

In the exponential function f(x) = ab^x, the base b represents the growth factor related to percent change in context.

Exponential Regression

A method of constructing an exponential function model for a data set using technology.

Transformation of Functions

The process of modifying the function f(x) = ab^x based on characteristics of a contextual scenario or data set.

Exponential Model

A mathematical model represented by the function f(x) = ab^x, used for analyzing data sets or predicting values.

Percent Increase

Start with the initial amount “a” and grow with a % increase:

y=a(1 + % increase)

Percent Decrease

Start with the initial amount “a” and decay with a % decrease:

y=a(1 - % decrease)

Half Life

An initial amount a that shrinks by half every h: f(t) = a(1/2)^t/h

Doubling Time

An initial amount a that doubles every d: 

f(t) = a(2)^t/d 

Equivalent Forms

Reveal different properties of the function