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Math Help - Differential Equation options question?

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    Differential Equation options question?

    I tried my best on this question: Differential Equation options question?-capture10.jpg Is my answer right? I'm just not sure because I keep getting formulas confused :/
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    Re: Differential Equation options question?

    No, your answer is not correct. If you want someone to say what you did wrong, then you will have to tell us what you did!
    Thanks from canyouhelp
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    Re: Differential Equation options question?

    Quote Originally Posted by HallsofIvy View Post
    No, your answer is not correct. If you want someone to say what you did wrong, then you will have to tell us what you did!
    With this one I struggled A LOT..because there were so many variables and I kept getting them confused :/ I tested each equation to see if it fit the question, but it took me a while and I wasn't sure how to test them. Can you help me with this?
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    Re: Differential Equation options question?

    Were you able to eliminate equation II? Why doesn't it work?

    - Hollywood
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    Re: Differential Equation options question?

    Quote Originally Posted by hollywood View Post
    Were you able to eliminate equation II? Why doesn't it work?

    - Hollywood
    Well, I think it's a red flag that it doesn't even have M, maximum performance, in it. Maybe that isn't a reason to eliminate it though?
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    Re: Differential Equation options question?

    Quote Originally Posted by canyouhelp View Post
    Well, I think it's a red flag that it doesn't even have M, maximum performance, in it. Maybe that isn't a reason to eliminate it though?
    You're guessing.

    What do you expect the value of $P_L$ to be as time goes to infinity?

    What do you expect the derivative to approach as $P_L$ approaches this value?
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    Re: Differential Equation options question?

    Quote Originally Posted by romsek View Post
    You're guessing.

    What do you expect the value of $P_L$ to be as time goes to infinity?

    What do you expect the derivative to approach as $P_L$ approaches this value?
    I think as the value of PL will increase when time approaches infinity. Right? Actually wouldn't it increase and then decrease? and the derivative of PL as PL curves would be a constant decreasing equation?
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    Re: Differential Equation options question?

    Quote Originally Posted by canyouhelp View Post
    I think as the value of PL will increase when time approaches infinity. Right? Actually wouldn't it increase and then decrease? and the derivative of PL as PL curves would be a constant decreasing equation?
    you are told $M$ is the maximum value $P_L$ will attain....
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    Re: Differential Equation options question?

    Quote Originally Posted by romsek View Post
    you are told $M$ is the maximum value $P_L$ will attain....
    Oh god, I'm an idiot. Okay so the value of PL will approach M as time approaches infinity. And I'm not sure what will happen with the derivative then. :/
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    Re: Differential Equation options question?

    Quote Originally Posted by canyouhelp View Post
    Oh god, I'm an idiot. Okay so the value of PL will approach M as time approaches infinity. And I'm not sure what will happen with the derivative then. :/
    If a function becomes constant, say at $P_L=M$, then what value must the derivative go to?
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    Re: Differential Equation options question?

    Quote Originally Posted by romsek View Post
    If a function becomes constant, say at $P_L=M$, then what value must the derivative go to?
    Is P'(L)= 0? I think.. :/
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    Re: Differential Equation options question?

    Quote Originally Posted by canyouhelp View Post
    Is P'(L)= 0? I think.. :/
    yes. Now there are two choices that satisfy these 2 conditions. You'll need to do a bit of work to figure out why one isn't correct.
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    Re: Differential Equation options question?

    Quote Originally Posted by romsek View Post
    yes. Now there are two choices that satisfy these 2 conditions. You'll need to do a bit of work to figure out why one isn't correct.
    Thank you so much! It took me forever but I separated all of them and eliminated the last one. I had to do the third one twice but it's derivative after separating doesn't equal 0. So it'd have to be option 2. I and II, right?
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    Re: Differential Equation options question?

    Quote Originally Posted by canyouhelp View Post
    Thank you so much! It took me forever but I separated all of them and eliminated the last one. I had to do the third one twice but it's derivative after separating doesn't equal 0. So it'd have to be option 2. I and II, right?
    Our condition is that as $P_L$ approaches $M$, $\dfrac{dP_L}{dt}$ approaches 0.

    Does II satisfy that?

    Does it look like III satisfies that?

    You don't have to do the separation to immediately rule out II and IV.
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    Re: Differential Equation options question?

    Quote Originally Posted by romsek View Post
    Our condition is that as $P_L$ approaches $M$, $\dfrac{dP_L}{dt}$ approaches 0.

    Does II satisfy that?

    Does it look like III satisfies that?

    You don't have to do the separation to immediately rule out II and IV.
    Um. I had I and III to begin with and I was told that was wrong...
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