Study Guides
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51.
Graphs of Exponential Functions Help
Introduction to Graphs of Exponential Functions A basic exponential function is of the form f ( x ) = a x , where a is any positive number except 1. The graph of ...
Source: McGraw-Hill Professional -
52.
Logarithms Help
Introduction to Logarithms A common question for investors is, “How long will it take for my investment to double?” If $1000 is invested so that it earns 8% interest, compounded annually, how long will it take to grow to $2000? To answer the question ...
Source: McGraw-Hill Professional -
53.
Simple Exponent and Logarithm Equations Help
Introduction to Simple Exponent and Logarithm Equations Equations with exponents and logarithms come in many forms. Sometimes more than one strategy will work to solve them. We will first solve equations of the form “log = number” and “log = ...
Source: McGraw-Hill Professional -
54.
Exponents and Logarithmic Equations Help
Introduction to Exponents and Logarithmic Equations For some logarithmic equations, a solution might be extraneous solution. That is, such a solution is a solution to the rewritten equations but not to the original equations. Some solutions to the rewritten ...
Source: McGraw-Hill Professional -
55.
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: McGraw-Hill Professional -
56.
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: McGraw-Hill Professional -
57.
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: McGraw-Hill Professional -
58.
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 half-life of a radioactive substance to describe how fast its radioactivity decays. For ...
Source: McGraw-Hill Professional -
59.
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: McGraw-Hill Professional -
60.
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 are ...
Source: McGraw-Hill Professional
