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m.auld64 Group Title

PLEASE HELP!!!

  • 2 years ago
  • 2 years ago

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  1. m.auld64 Group Title
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    Hospital officials estimate that approximately N(p)=p^2+5p+900 people will seek treatment in an emergency room each year if the population of the community is thousand. The population is currently 20,000 and is growing at the rate of 1,200 per year. At what rate is the number of people seeking emergency room treatment increasing?

    • 2 years ago
  2. TheFigure Group Title
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    Did you forget something between the words "is" and "thousand"?

    • 2 years ago
  3. No-data Group Title
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    I think you're looking for \[\frac{dN}{dt}\]

    • 2 years ago
  4. No-data Group Title
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    which can be found by looking at \[\frac{dN}{dt}=\frac{dN}{dp}\frac{dp}{dt}\]

    • 2 years ago
  5. TheFigure Group Title
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    First, start with your function\[N(p)=p ^{2}+5p+900\] Let's take a derivative of both sides to unlock the rates of change that are related\[\frac{d}{dt}N(p)=\frac{d}{dt}(p ^{2}+5p+900)\] Then we can simplify to this:\[\frac{dN}{dt}=2p \frac{dp}{dt}+5\] From here, let's plug in what we know:\[1,200=2(20,000) \frac{dp}{dt}+5\] From here, you can solve for dp/dt

    • 2 years ago
  6. m.auld64 Group Title
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    so why did dp/dt only come up with the p^2 term and not the 5p term

    • 2 years ago
  7. TheFigure Group Title
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    I'm wondering about that myself actually...

    • 2 years ago
  8. m.auld64 Group Title
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    and I'm actually looking for dN/dt according to the way this is making me input my answer

    • 2 years ago
  9. TheFigure Group Title
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    Good gawd - then I really messed that one up... lol

    • 2 years ago
  10. m.auld64 Group Title
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    haha its all good I've been messing this one up for about an hour

    • 2 years ago
  11. TheFigure Group Title
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    Let's try that one again... From the top - take two!

    • 2 years ago
  12. TheFigure Group Title
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    Here is our function:\[N(p)=p^2+5p+900\] Let's first identify some things what we are given, and we'll identify what they're asking us for (whenever I skip that, I screw things up).

    • 2 years ago
  13. m.auld64 Group Title
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    right

    • 2 years ago
  14. m.auld64 Group Title
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    that was right to the function not to you screwing up by the way haha

    • 2 years ago
  15. TheFigure Group Title
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    The population is currently 20,000; so p = 20,000 It is growing at a rate of 1,200 per year; so dp/dt = 1,200

    • 2 years ago
  16. TheFigure Group Title
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    They're asking for the the rate at which the number of people seeking medical attention is increasing; so dN/dt = ?

    • 2 years ago
  17. TheFigure Group Title
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    That's what we're trying to find. :)

    • 2 years ago
  18. m.auld64 Group Title
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    ok well what if we take what you had a second ago 2(20)(dp/dt) +5 and plug in 1200 for dp/dt and yes thats what we are trying to find hha

    • 2 years ago
  19. m.auld64 Group Title
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    well actually thats just going to give us a ridiculously huge number

    • 2 years ago
  20. TheFigure Group Title
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    But, will the number make sense?

    • 2 years ago
  21. TheFigure Group Title
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    What did you get?

    • 2 years ago
  22. m.auld64 Group Title
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    no it was like 48 million

    • 2 years ago
  23. TheFigure Group Title
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    \[\frac{d}{dt}N(p)=\frac{d}{dt}(p^2+5p+900)\]Lets plug these things into the right places this time... \[\frac{d}{dt}N(p)=2p \frac{dp}{dt}+5\frac{dp}{dt}\] \[\frac{dN}{dt}=2(20,000)(1,200)+5(1,200)\]

    • 2 years ago
  24. m.auld64 Group Title
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    ya thats what i did

    • 2 years ago
  25. TheFigure Group Title
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    Oh man... I got nothing... And nothing was left out of the question?

    • 2 years ago
  26. m.auld64 Group Title
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    ya i don't get it either man thanks anyway

    • 2 years ago
  27. TheFigure Group Title
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    I'm going to take a look at this one on the calculator really quick, just to see if that will shine a little light on this one.

    • 2 years ago
  28. TheFigure Group Title
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    Wait a sec...

    • 2 years ago
  29. TheFigure Group Title
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    You originally wrote: "Hospital officials estimate that approximately N(p)=p^2+5p+900 people will seek treatment in an emergency room each year if the population of the community is thousand. The population is currently 20,000 and is growing at the rate of 1,200 per year. At what rate is the number of people seeking emergency room treatment increasing?"

    • 2 years ago
  30. TheFigure Group Title
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    Did you instead mean: "Hospital officials estimate that approximately N(p)=p^2+5p+900 people will seek treatment in an emergency room each year if the population of the community IN thousands." ?

    • 2 years ago
  31. TheFigure Group Title
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    Because if you did, then we should be plugging in 20 instead of 20,000. Actually, that may fix the problem. :)

    • 2 years ago
  32. TheFigure Group Title
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    If the function is set up to inherently measure in thousands, then by typing in 20,000 - we're accidentally making the population 20,000,000.

    • 2 years ago
  33. Chlorophyll Group Title
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    @TheFigure you already reached the answer: 48,006,000 people seek for emergency care per year!

    • 2 years ago
  34. TheFigure Group Title
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    But he would be entering the answer in wrong if he had those extra zeros attached to the back of it.

    • 2 years ago
  35. Chlorophyll Group Title
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    You've been right since 30 min before :)

    • 2 years ago
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