Chapter 3 - Exponential, Logistic, and Logarithmic Functions"In this chapter, we study three interrelated families of functions: exponential, logistic, and logarithmic functions. Polynomial functions, rational functions, and power func- tions with rational exponents are algebraic functions — functions obtained by adding, subtracting, multiplying, and dividing constants and an independent variable, and rais- ing expressions to integer powers and extracting roots. In this chapter and the next one, we explore transcendental functions, which go beyond, or transcend, these algebraic operations.
Just like their algebraic cousins, exponential, logistic, and logarithmic functions have wide application. Exponential functions model growth and decay over time, such as unrestricted population growth and the decay of radioactive substances. Logistic functions model restricted population growth, certain chemical reactions, and the spread of rumors and diseases. Logarithmic functions are the basis of the Richter scale of earthquake intensity, the pH acidity scale, and the decibel meas- urement of sound. The chapter closes with a study of the mathematics of finance, an application of exponential and logarithmic functions often used when making investments." (Demana, Franklin D. "Chapter 3." Precalculus: Graphical, Numerical, Algebraic. 7th ed. Boston: Addison-Wesley, 2007. 275. Print.) |
"The loudness of a sound we hear is based on the intensity of the associated sound wave. This sound intensity is the energy per unit time of the wave over a given area, measured in watts per square meter (W/m2). The intensity is greatest near the source and decreases as you move away, whether the sound is rustling leaves or rock music. Because of the wide range of audible sound intensities, they are generally converted into decibels, which are based on logarithms. See page 307."
(Demana, Franklin D. "Chapter 3." Precalculus: Graphical, Numerical, Algebraic. 7th ed. Boston: Addison-Wesley, 2007. 275. Print.) |
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Lesson 3.1 - Exponential and Logistic Functions
This lesson will cover exponential functions, the natural base e, logistic functions, population models, and graphs of these functions. Lesson 3.2 - Exponential and Logistic Modeling
This lesson covers constant percentage rate and exponential functions, exponential growth and decay models, using regression to model population, and other logistic models. Lesson 3.3 - Logarithmic Functions and their Graphs
This lesson will cover inverses of exponential functions, common logarithms base 10, natural logarithms base e, graphs of logarithmic functions, and measuring sound using decibels. |
Lesson 3.4 - Properties of Logarithmic Functions
This lesson covers properties of logarithms, change of base, graphs of logarithmic functions with base b, and re-expressing data. Lesson 3.5 - Equation Solving and Modeling
This lesson covers solving exponential equations, solving logarithmic equations, orders of magnitude and logarithmic models, Newton's Law of Cooling, and logarithmic re-expression. Lesson 3.6 - Mathematics of Finance
This lesson covers interest compounded annually, interest compounded k times per year, interest compounded continuously, annual percentage yield, annuities - future value, and loans and mortgages - present value. |
