Lial/Hungerford/Holcomb/Mullins: Mathematics with Applications 11e Finite Mathematics with Applications 11e Copyright ©2015 Pearson Education, Inc. All right reserved.

Exponential and Logarithmic Functions Chapter 4 Exponential and Logarithmic Functions Copyright ©2015 Pearson Education, Inc. All right reserved.

Exponential Functions Section 4.1 Exponential Functions Copyright ©2015 Pearson Education, Inc. All right reserved.

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Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Consider the function (a) Rewrite the rule of g so that no minus signs appear in it. Solution: By the definition of negative exponents, (b) Graph g(x). Solution: Either use a graphing calculator or graph by hand in the usual way, as shown below. Copyright ©2015 Pearson Education, Inc. All right reserved.

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Applications of Exponential Functions Section 4.2 Applications of Exponential Functions Copyright ©2015 Pearson Education, Inc. All right reserved.

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Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Finance When money is placed in a bank account that pays compound interest, the amount in the account grows exponentially. Suppose such an account grows from $1000 to $1316 in 7 years. (a) Find a growth function of the form that gives the amount in the account at time t years. Solution: The values of the account at time are given; that is, Solve the first of these equations for So the rule of f has the form Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Finance When money is placed in a bank account that pays compound interest, the amount in the account grows exponentially. Suppose such an account grows from $1000 to $1316 in 7 years. (a) Find a growth function of the form that gives the amount in the account at time t years. Solution: Now solve the equation So the rule of the function is (b) How much is in the account after 12 years? Solution: Copyright ©2015 Pearson Education, Inc. All right reserved.

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Logarithmic Functions Section 4.3 Logarithmic Functions Copyright ©2015 Pearson Education, Inc. All right reserved.

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Copyright ©2015 Pearson Education, Inc. All right reserved. Example: To find log 10,000, ask yourself, “To what exponent must 10 be raised to produce 10,000?” Since we see that Similarly, Copyright ©2015 Pearson Education, Inc. All right reserved.

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Logarithmic and Exponential Equations Section 4.4 Logarithmic and Exponential Equations Copyright ©2015 Pearson Education, Inc. All right reserved.

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Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Solve Solution: First, use the quotient property of logarithms to write the right side as a single logarithm: The fact on the preceding slide now shows that Since log x is not defined when the only possible solution is Copyright ©2015 Pearson Education, Inc. All right reserved.

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