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Math Help - Find the value of y when x=2.

  1. #1
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    Find the value of y when x=2.

    Given that dy/dx=a*e^(-x)+1 and that when x=0, dy/dx=3 and y=5, find the value of y when x=2.
    I wasn't really sure where to start with this problem ...
    So I subbed in x=0 and dy/dx=3 into the derivative to find a, which ended up being a=2.
    Then I anti differentiated dy/dx to get y=a*e^(-x)+x.
    I subbed in y=5 and x=0 into that equation to find a, which was a=-5.
    And then I didn't really know what to do from there.
    I don't even know if what I did was necessary to answer the question either.
    Thank you so much in advance for your help!
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  2. #2
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    Re: Find the value of y when x=2.

    Quote Originally Posted by juliacoolness View Post
    Given that dy/dx=a*e^(-x)+1 and that when x=0, dy/dx=3 and y=5, find the value of y when x=2.
    I wasn't really sure where to start with this problem ...
    So I subbed in x=0 and dy/dx=3 into the derivative to find a, which ended up being a=2.
    Then I anti differentiated dy/dx to get y=a*e^(-x)+x.
    I subbed in y=5 and x=0 into that equation to find a, which was a=-5.
    And then I didn't really know what to do from there.
    I don't even know if what I did was necessary to answer the question either.
    Thank you so much in advance for your help!
    1. You made a tiny mistake by calculating y:

    \dfrac{dy}{dx}=2 \cdot e^{-x} +1 ~\implies~y=-2 \cdot e^{-x}+x+c

    2. Now you know that f(0) = 5. That means:

    f(0)=-2+c=5~\implies~c=7

    3. So the complete equation of the function is:

    y = f(x) = -2 \cdot e^{-x}+x+7

    4. Now plug in x = 2.
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  3. #3
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    Re: Find the value of y when x=2.

    Thanks so much mate.
    I'm so glad you pointed that out to me.
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