anonymous
  • anonymous
PLEASE HELP!!!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
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?
anonymous
  • anonymous
Did you forget something between the words "is" and "thousand"?
anonymous
  • anonymous
I think you're looking for \[\frac{dN}{dt}\]

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anonymous
  • anonymous
which can be found by looking at \[\frac{dN}{dt}=\frac{dN}{dp}\frac{dp}{dt}\]
anonymous
  • anonymous
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
anonymous
  • anonymous
so why did dp/dt only come up with the p^2 term and not the 5p term
anonymous
  • anonymous
I'm wondering about that myself actually...
anonymous
  • anonymous
and I'm actually looking for dN/dt according to the way this is making me input my answer
anonymous
  • anonymous
Good gawd - then I really messed that one up... lol
anonymous
  • anonymous
haha its all good I've been messing this one up for about an hour
anonymous
  • anonymous
Let's try that one again... From the top - take two!
anonymous
  • anonymous
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).
anonymous
  • anonymous
right
anonymous
  • anonymous
that was right to the function not to you screwing up by the way haha
anonymous
  • anonymous
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
anonymous
  • anonymous
They're asking for the the rate at which the number of people seeking medical attention is increasing; so dN/dt = ?
anonymous
  • anonymous
That's what we're trying to find. :)
anonymous
  • anonymous
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
anonymous
  • anonymous
well actually thats just going to give us a ridiculously huge number
anonymous
  • anonymous
But, will the number make sense?
anonymous
  • anonymous
What did you get?
anonymous
  • anonymous
no it was like 48 million
anonymous
  • anonymous
\[\frac{d}{dt}N(p)=\frac{d}{dt}(p^2+5p+900)\]Lets plug these things into the right places this time... \[\frac{d}{dt}N(p)=2p \frac{dp}{dt}+5\frac{dp}{dt}\] \[\frac{dN}{dt}=2(20,000)(1,200)+5(1,200)\]
anonymous
  • anonymous
ya thats what i did
anonymous
  • anonymous
Oh man... I got nothing... And nothing was left out of the question?
anonymous
  • anonymous
ya i don't get it either man thanks anyway
anonymous
  • anonymous
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.
anonymous
  • anonymous
Wait a sec...
anonymous
  • anonymous
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?"
anonymous
  • anonymous
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." ?
anonymous
  • anonymous
Because if you did, then we should be plugging in 20 instead of 20,000. Actually, that may fix the problem. :)
anonymous
  • anonymous
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.
anonymous
  • anonymous
@TheFigure you already reached the answer: 48,006,000 people seek for emergency care per year!
anonymous
  • anonymous
But he would be entering the answer in wrong if he had those extra zeros attached to the back of it.
anonymous
  • anonymous
You've been right since 30 min before :)

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