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Thread: Differentiation of Exponential Functions: v'(10)=37,500^e10/8

  1. #1

    Smile Differentiation of Exponential Functions: v'(10)=37,500^e10/8

    Hello everyone,

    Can you please explain how to solve v'(10)=37,500^e10/8?

    A tapestry purchased in 1998 for $300,000 is estimated to be worth v(t)=300,000e^t/8 dollars after t years. At what rate will the tapestry be appreciating in 2008?


    I start v'(t)=300,000e^t/8*1/8=37,500e^t/8
    t=2008-1998=10
    v'(10)=37,500^e10/8

    * I figured it out 37,500 * 3.49034~130,888
    Last edited by SnappleG; 11-02-2013 at 12:44 AM. Reason: Solved

  2. #2
    Senior Member
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    Quote Originally Posted by SnappleG View Post
    Hello everyone,

    Can you please explain how to > > > solve < < <v'(10)=37,500^e10/8?

    A tapestry purchased in 1998 for $300,000 is estimated to be worth v(t)=300,000e^t/8 dollars after t years.
    At what rate will the tapestry be appreciating in 2008?


    I start v'(t)=300,000e^t/8*1/8=37,500e^t/8


    t=2008-1998=10

    v'(10)=37,500^e10/8

    Can you please explain step by step how to > > > solve < < < v'(10)=37,500^e10/8? Thank you!

    I have an example: v'(4)=112,500e^4/2

    The answer is ~ 831,269

    I just don't understand how you come to ~ 831,269
    You put the "^" in the wrong places, you are missing grouping symbols around exponents,
    and you are "evaluating," not "solving."

    Here is most of your post with some amendments:


    Evaluate 37,500e^(10/8).

    A tapestry purchased in 1998 for $300,000 is estimated to be worth v(t)=300,000e^(t/8) dollars after t years.
    At what rate will the tapestry be appreciating in 2008?


    I start v'(t) = 300,000e^(t/8)*(1/8) = 37,500e^(t/8)

    t = 2008 - 1998 = 10

    v'(10)= 37,500e^(10/8)

    Can you please explain step by step how to evaluate v'(10) = 37,500e^(10/8)?

    I have an example: v'(4) = 112,500e^(4/2)

    The answer is ~ 831,269

    I just don't understand how you come to ~ 831,269
    SnappleG, now that you know that you should enter your example as "112500e^(4/2)" or just

    as "112500e^(2)" in a calculator that shows that kind of display, try that first, and then come

    back to this thread to tell us if your display gives a value that will round to 831,269.

  3. #3
    Quote Originally Posted by lookagain View Post
    You put the "^" in the wrong places, you are missing grouping symbols around exponents,
    and you are "evaluating," not "solving."

    SnappleG, now that you know that you should enter your example as "112500e^(4/2)" or just

    as "112500e^(2)" in a calculator that shows that kind of display, try that first, and then come

    back to this thread to tell us if your display gives a value that will round to 831,269.
    Thank you, I usually use a basic calculator - at least all previous problems I had to solve & evaluate did not need any complex calculations. English is my 2nd language and that is way I misused solve.

  4. #4
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    Quote Originally Posted by SnappleG View Post
    Thank you, I usually use a basic calculator - at least all previous problems I had to solve & evaluate did not need any complex calculations. English is my 2nd language and that is way I misused solve.
    On my calculator, the [tex]e^x[/tex] function is the inverse of the [tex]\ln[/tex] function. That is, "<SHIFT>-ln".

    Using the built-in Windows calculator set to "Scientific" on its View menu, enter x, then click the "Inv" box and the "ln" key.
    DrPhil (not the TV guy)
    If we knew what we were doing,we wouldn't have to do it

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