Page 2: Real-World Applications and Growth Factor Calculations

This page explores practical applications of exponential growth and decay through various scenarios including bacterial cultures, algae growth, and car depreciation.

Example: A bacterial culture starting with 20 bacteria triples hourly, demonstrating exponentielles wachstum beispiel alltag.

Definition: Growth percentage can be positive (growth) or negative (decay), affecting the growth factor calculation.

Highlight: The page includes exercises on calculating growth factors for different percentage changes and applying them to real-world situations.

Page 3: Solutions and Detailed Calculations

This page provides comprehensive solutions to growth factor problems and demonstrates practical applications in various scenarios.

Example: A car's value depreciation is calculated using a 15% annual decrease, showing exponentielle abnahme beispiel.

Vocabulary: Growth factor (Wachstumsfaktor) - The multiplier used to calculate exponential growth or decay.

Highlight: Solutions demonstrate how to calculate complex growth scenarios including compound effects over multiple time periods.

Page 4: Advanced Applications and Function Types

This page concludes with advanced applications and different types of mathematical functions related to growth and decay.

Definition: Functions can be classified as linear, quadratic, or exponential based on their growth patterns.

Example: f$x$ = 6.5^x represents exponential growth where the initial value of 6 increases fivefold each period.

Highlight: The page demonstrates how to distinguish between different types of growth patterns using tables and functions.

Page 1: Growth Factors and Applications

This page introduces fundamental concepts of exponential growth and decay through practical exercises involving bacterial colonies and radioactive decay.

Definition: The growth factor $b$ represents the multiplier that determines how a quantity changes over each time period in exponential growth or decay.

Example: For bacterial colonies, growth is calculated using initial quantities and multiplication factors, such as doubling or tripling per hour.

Highlight: Problems include calculating bacterial growth over various time periods and radioactive decay using half-life concepts.

Vocabulary: Half-life (Halbwertszeit) - The time required for a quantity to reduce to half its initial value.