Algebra 2: Exponents & Logarithms Quiz

Questions and Answers

What is exponential growth?

A type of decay where the population decreases rapidly

A fixed increase of a population over time

Growth pattern that varies with time

Growth pattern in which individuals in a population reproduce at a constant rate (correct)

Define exponential decay.

When an initial amount decreases by the same percent over a given period of time.

The growth rate is the ______ by which a quantity increases (or decreases) over time.

addend

What is the decay factor?

1 minus the percent rate of change, expressed as a decimal. Signup and view all the answers

What is the basic form of exponential functions?

f(x) = b^x, where b is a positive constant. Signup and view all the answers

If b is a positive number other than 1, then b^x = b^y if and only if x = y.

True Signup and view all the answers

What are exponential inequalities?

Inequalities that involve a variable exponent Signup and view all the answers

What does the logarithm base b of a number x represent?

The power to which b must be raised to equal x. Signup and view all the answers

Logarithmic functions behave differently than other parent functions.

False Signup and view all the answers

What is the equality property for logarithmic equations?

If b, x, and y are positive numbers with b≠1, then log_b(x) = log_b(y) if and only if x = y. Signup and view all the answers

In logarithmic functions, if a is greater than 1, then if x > y, it implies x < y.

False Signup and view all the answers

Study Notes

Exponential Growth and Decay

Exponential Growth: Individuals in a population reproduce at a constant rate, leading to rapid increase.
Exponential Decay: An initial amount decreases consistently by a fixed percentage over time.

Growth and Decay Factors

Growth Factor: The addend that represents the rate of increase or decrease; a 10% annual investment yield is an example where the total multiplies by 1.10 (110%).
Decay Factor: Calculated as 1 minus the percentage change expressed as a decimal in decay scenarios.

Transformations of Functions

Exponential Functions Transformation: The base function f(x) = b^x can be altered through vertical/horizontal shifts and graph reversals, modifying its appearance but not its fundamental characteristics.
Logarithmic Functions Transformation: Similar transformations apply to logarithmic graphs, allowing shifts, stretches, compressions, and reflections without altering shape.

Properties of Exponential Functions

Property of Equality: For a positive base b (b ≠ 1), if b^x = b^y, then x must equal y; for instance, if 2^x = 2^8, then x = 8.
Property of Inequality: Exponential inequalities involve variable exponents and are essential for comparing quantities through repeated multiplication.

Properties of Logarithms

Logarithmic Properties: The logarithm base b of a number x indicates the power to which b must be raised to reach x. Key properties include:
- Product Rule: The log of a product equals the sum of the logs of the factors.

Properties of Equality and Inequality in Logarithms

Equality Properties:
- For exponential equations, if b is a positive number (b ≠ 1), bx = by implies x = y by matching bases and equating exponents.
- For logarithmic equations, log_b(x) = log_b(y) holds true when x = y, with b, x, and y being positive numbers (b ≠ 1).
Inequality Properties: If a > 1, then inequalities involving logarithmic expressions follow standard comparison rules (x > y or x < y).

Description

Test your understanding of exponents and logarithms with this flashcard quiz. Learn definitions and key concepts such as exponential growth, decay, and growth factors. Perfect for Algebra 2 students looking to reinforce their knowledge.