6: Exponential functions

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Lynda Zenati
Olive Harvey College

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6.1: Introduction to exponential functions
This page explores applications of exponential growth and decay in finance and environmental scenarios. It starts with a calculation example of an $8,000 investment growing at 6% annually. It then examines the 55% annual decay of substance X in a polluted lake. Finally, it compares population trends in two towns, Alphaville and Betatown, showcasing one town's growth alongside the other's decline, while encouraging readers to calculate their population changes and potential convergence.
6.2: The logarithm function and its applications
This page reviews logarithms and exponential expressions, focusing on converting between forms and evaluating logarithms without a calculator. It includes tasks for determining the truth of expressions and solving equations, highlighting the relationship between logarithms and exponentials. Mastery of these concepts is crucial for advanced mathematics.
6.3: Logarithms and exponential models
This page covers exponential growth and decay, highlighting applications in population dynamics with annual growth rates and constant doubling times. It discusses radioactive decay using cobalt-60, deriving expressions for remaining quantities and decay timeframes. The page also explores continuous growth functions and the conversion of exponential forms, alongside calculating continuous growth rates.
6.4: Logarithmic Functions and Applications
This page covers exponential and logarithmic functions, focusing on the graphs of $y=e^x$ and $y=\ln x$, including their asymptotes and interconnections. It introduces pH as a logarithmic measure of acidity, providing exercises for calculating ion concentrations across various pH levels. Additionally, the page encourages readers to identify expressions for specific exponential or logarithmic function graphs.
6.5: Comparing power, exponential and log functions
This page provides an analysis of functions, their graphs, and growth rates as $x$ approaches infinity. It includes identifying and matching functions to their graphs, classifying them based on provided tables, and comparing growth rates between specific functions like $y=x^{\frac{1}{2}}$, $y=\ln x$, and $y=x^2$. The page concludes with an examination of the end behavior of certain functions in both positive and negative directions of $x$.
6.6: Comparing linear and exponential functions Graphs of exponential functions
This page explores revenue growth of a grocery store from 2020 to 2030 using linear and exponential models, detailing calculations for future revenues and growth equations. It highlights the advantages of exponential growth and evaluates different functions based on data. Additionally, it presents a math tutoring business's bank account balance over time, illustrating the concepts discussed.
6.7: Compound interest and the number e
This page explains how compounding influences interest on a $5,000 bank account at a 6% nominal interest rate, examining both annual and quarterly compounding frequencies and their impacts over 10 years. It introduces continuous compounding and contrasts it with discrete methods. The page also covers exponential growth in epidemics, offering related examples and calculations. Furthermore, it discusses revenue growth for an online store under varying compounding scenarios.

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