1. Lial/Hungerford/Holcomb/Mullins: Mathematics with Applications 11e Finite Mathematics with Applications 11e
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2. Exponential and Logarithmic Functions
Chapter 4
Exponential and Logarithmic
Functions
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3. Exponential Functions
Section 4.1
Exponential Functions
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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.
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17. Applications of Exponential Functions
Section 4.2
Applications of Exponential Functions
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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
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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:
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25. Logarithmic Functions
Section 4.3
Logarithmic Functions
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Example:
To find log 10,000, ask yourself, “To what exponent must 10 be raised to produce 10,000?” Since we see that Similarly,
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41. Logarithmic and Exponential Equations
Section 4.4
Logarithmic and Exponential
Equations
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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
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