Unit 7 - Lesson 9: Exam Review

Flashcards covering key vocabulary and concepts from Unit 7, Lesson 9, focusing on exponential and logarithmic functions and equations.

y = abx

Models exponential growth when a > 0 and b > 1.

y = abx

Models exponential decay when 0 < b < 1.

Equivalence of Logarithms and Exponents

Logarithms are exponents, logb a = c if and only if bc = a.

Inverse Functions

The exponential function y = bx and the logarithmic function y = logb x are inverse functions.

Product Property of Logarithms

The properties that allow logarithms to be added when multiplying original values.

Quotient Property of Logarithms

The properties that allow logarithms to be subtracted when dividing original values.

y = loge x = ln x

The inverse of y = ex.

Exponential Equation

An equation in the form bx = a, where the exponent includes a variable.

Logarithmic Equation

An equation that includes one or more logarithms involving a variable.

Common Logarithm

The base 10 logarithm.

Change of Base Formula

The formula that converts a logarithm of one base to another.

Exponential Function

The general form of an exponential function is y = abx, where x is a real number, a ≠ 0, b > 0, and b ≠ 1.

Exponential Growth

When b > 1, the function models exponential growth, and b is the growth factor.

Exponential Decay

When 0 < b < 1, the function models exponential decay, and b is the decay factor.

Continuously Compounded Interest Formula

A = Pert, where P is the principal, r is the annual interest rate, and t is time in years.