Study Guides

31.
The Change of Base Formula Help
Introduction to The Change of Base Formula There are countless bases for logarithms but calculators usually have only two logarithms—log and ln. How can we use our calculators to approximate log 2 5? We ...
Source: McGrawHill Professional 
32.
Applications of Logarithm and Exponential Equations Help
Introduction to Applications of Logarithm and Exponential Equations Now that we can solve exponential and logarithmic equations, we can solve many applied problems. We will need the compound growth formula for an investment earning interest rate r ...
Source: McGrawHill Professional 
33.
Finding the Growth Rate Help
Introduction to Finding the Growth Rate We can find the growth rate of a population if we have reason to believe that it is growing exponentially and if we know the population level at two different times. We will use the first population level as n
Source: McGrawHill Professional 
34.
Radioactive Decay  Review and Examples Help
Introduction to Radioactive Decay Some radioactive substances decay at the rate of nearly 100% per year and others at nearly 0% per year. For this reason, we use the halflife of a radioactive substance to describe how fast its radioactivity decays. For ...
Source: McGrawHill Professional 
35.
Applications of Systems of Equations Help
Applications of Systems of Equations Systems of two linear equations can be used to solve many kinds of word problems. In these problems, two facts will be given about two variables. Each pair of facts can be represented by a linear equation. This gives us a ...
Source: McGrawHill Professional 
36.
Graphical Solution to System of Equations Help
Introduction to Graphical Solution to System of Equations Two lines in the plane either intersect in one point, are parallel, or are really the same line. Until now, our lines have intersected in one point. When solving a system of two linear equations that ...
Source: McGrawHill Professional 
37.
Systems of Inequalities Help
Introduction to Systems of Inequalities The solution (if any) for a system of inequalities is usually a region in the plane. The solution to a polynomial inequality (the only kind in this book) is the region above or below the curve. We will begin with linear ...
Source: McGrawHill Professional 
38.
Coterminal and Reference Angles Help
Introduction to Coterminal and Reference Angles Two angles are coterminal if their terminal sides are the same. For example, the terminal sides of the angles 300° and −60° are the same. See Figure 13.3.
Source: McGrawHill Professional 
39.
Trigonometric Functions Help
Introduction to Trigonometric Functions There are six trigonometric functions, but four of them are written in terms of two of the main functions—sine and cosine. Although trigonometry was developed to solve problems involving triangles, there is a very ...
Source: McGrawHill Professional 
40.
Graphs of Other Trigonometric Functions Help
Introudction to Graphs of Other Trigonometric Functions Because csc x = 1/sin x , the graph of y = csc x has a vertical asymptote everywhere y = sin x has an x intercept (where sin x = 0). ...
Source: McGrawHill Professional