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Math Help - Exponential Functions

  1. #1
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    Exponential Functions

    Once the initial publicity surrounding the release of a new book is over, sales of the hardcover edition tend to decrease exponentially. At the time publicity was discontinued, a certain book was experiencing sales of 25,000 copies per month. One month later, sales of the book had dropped to 10,000 copies per month. What will the sales be after 1 more month?
    I have no idea on how to solve this problem. Please show me a step by step solution! The answer is 4000.

    And also need assistance with the following question...

    Find f(2) if f(x) = e^{kx} and f(1) = 20.

    Here's what I did...

     20 = e^{k \times 1}
     e^{20} = e^{k \times 1}
     20 = e

     f(2) = e^{20 \times 2}
     f(2) = 2.3539 x 10^{17}

    ...and textbook answer is 400.
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  2. #2
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    For your second question: 20=f(1)=e^k\rightarrow k=\log 20 so f(2)=e^{2\cdot \log 20}=\left(e^{\log 20}\right)^2=20^2=\boxed{400}.
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  3. #3
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    Quote Originally Posted by Macleef View Post
    I have no idea on how to solve this problem. Please show me a step by step solution! The answer is 4000.

    And also need assistance with the following question...

    Find f(2) if f(x) = e^{kx} and f(1) = 20.

    Here's what I did...

     20 = e^{k \times 1}
     e^{20} = e^{k \times 1}
     20 = e

     f(2) = e^{20 \times 2}
     f(2) = 2.3539 x 10^{17}

    ...and textbook answer is 400.
    Step 1 to Step 2 is wrong. How have you turned 20 into e^{20}?


    You should have

    20 = e^k

    k = \ln{20}.


    Therefore f(x) = e^{x\ln{20}} = e^{\ln{20^x}} = 20^x.

    Thus f(2) = 20^2 = 400.
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  4. #4
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    Quote Originally Posted by Macleef View Post
     20 = e^{k \times 1}
     e^{20} = e^{k \times 1}
     20 = e

     f(2) = e^{20 \times 2}
     f(2) = 2.3539 x 10^{17}

    ...and textbook answer is 400.
    How did you get that?? If you take a look at the first two lines you can see that it just can be true. (It would mean that 20=e^{20}..) I suppose that you meant  20 = k in the third line, then it would at least come from the line above and the other two lines would come from that...

    Do you understand the solution?
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