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    Graphing ExponentialFunctions

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    Example 1

    Graph the following two equations: f(x)= ,f(x)= 44

    Draw the asymptotes.

    xx

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    Transformations of ExponentialFunctions

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    Example Use the graph of f(x)=4 to obtain the graph of g(x)=4 3.What is the domain and range of each function?

    x x

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    Example 2Use the graph of f(x)=4 to obtain the graph of g(x)=4

    Find the domain and range for the g(x) function.

    x x

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    Example Use the graph of f(x)=4 to obtain the graph of g(x)=2 4

    Find the domain and range for the g(x) function.

    x x

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    The Natural Base e

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    1The values of 1+ for increasingly

    large values of n. As n the

    approximate value of e to nine decimal

    places is e 2.718281827.

    The irrational number e, approximately

    2.72, is called the natura

    n

    n

    l base. The

    function f(x)=e is called the natural

    exponential function.

    x

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    Example

    .8

    The population of a small polynesian island can be modeled by

    the equation f(x)=8e . Round off your answers to the

    nearest integer.

    a. How many people originally went to this small island? (x=0)

    b. H

    x

    ow many people will be living on this island 10 years laterdue to general population growth with no new immigration.

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    Compound Interest

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    Compound interest is interest computed on your original investment

    as well as on any accumulated interest. The sum of money is called

    the principal, P. It is invested at an annual percentage rate r, and

    compounded once a year.

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    Sometimes interest is compounded semiannually, monthly, quarterly, etc. This introduces

    the variable for the number of compounding periods per year. The formula is then adjusted

    to take this into acc

    n

    ount the number of compunding periods in a year. If there are compuonding

    periods per year, in each time period the interest rate is = and there are time periods in years.

    The results in the f

    n

    ri nt t

    n

    ollowing formula for the balance, A, after t years is

    A=P 1

    nt

    rn

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    Continuous Compounding of Interest

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    Example

    Find the accumulated value of an investment of $15,000

    for 2 years at an interest rate of 3.2% if the money is

    a. compounded semiannually

    b. compounded quarterly

    c. compounded monthlyd. compounded continuously

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    (a)

    (b)

    (c)

    (d)

    3For the graph of f(x)=4 1, What is the domain and range?x

    : ( 1, ), : ( 1, )

    : ( , ), : ( 1, ): ( , ), : ( , )

    :[ 1, ), :[ 1, )

    D R

    D R

    D R

    D R

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    (a)

    (b)

    (c)

    (d)

    Find the accumulated value of a CD of $20,000 for 3 years

    at an interest rate of 3.1% if the money is compounded continuously?

    50,690

    218,760,384

    21,949

    21,860