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m.auld64 Group TitleBest ResponseYou've already chosen the best response.0
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

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
Did you forget something between the words "is" and "thousand"?
 2 years ago

Nodata Group TitleBest ResponseYou've already chosen the best response.1
I think you're looking for \[\frac{dN}{dt}\]
 2 years ago

Nodata Group TitleBest ResponseYou've already chosen the best response.1
which can be found by looking at \[\frac{dN}{dt}=\frac{dN}{dp}\frac{dp}{dt}\]
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
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

m.auld64 Group TitleBest ResponseYou've already chosen the best response.0
so why did dp/dt only come up with the p^2 term and not the 5p term
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
I'm wondering about that myself actually...
 2 years ago

m.auld64 Group TitleBest ResponseYou've already chosen the best response.0
and I'm actually looking for dN/dt according to the way this is making me input my answer
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
Good gawd  then I really messed that one up... lol
 2 years ago

m.auld64 Group TitleBest ResponseYou've already chosen the best response.0
haha its all good I've been messing this one up for about an hour
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
Let's try that one again... From the top  take two!
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
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

m.auld64 Group TitleBest ResponseYou've already chosen the best response.0
that was right to the function not to you screwing up by the way haha
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
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

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
They're asking for the the rate at which the number of people seeking medical attention is increasing; so dN/dt = ?
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
That's what we're trying to find. :)
 2 years ago

m.auld64 Group TitleBest ResponseYou've already chosen the best response.0
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

m.auld64 Group TitleBest ResponseYou've already chosen the best response.0
well actually thats just going to give us a ridiculously huge number
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
But, will the number make sense?
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
What did you get?
 2 years ago

m.auld64 Group TitleBest ResponseYou've already chosen the best response.0
no it was like 48 million
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
\[\frac{d}{dt}N(p)=\frac{d}{dt}(p^2+5p+900)\]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

m.auld64 Group TitleBest ResponseYou've already chosen the best response.0
ya thats what i did
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
Oh man... I got nothing... And nothing was left out of the question?
 2 years ago

m.auld64 Group TitleBest ResponseYou've already chosen the best response.0
ya i don't get it either man thanks anyway
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
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

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
Wait a sec...
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
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

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
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

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
Because if you did, then we should be plugging in 20 instead of 20,000. Actually, that may fix the problem. :)
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
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

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.0
@TheFigure you already reached the answer: 48,006,000 people seek for emergency care per year!
 2 years ago

TheFigure Group TitleBest ResponseYou've already chosen the best response.4
But he would be entering the answer in wrong if he had those extra zeros attached to the back of it.
 2 years ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.0
You've been right since 30 min before :)
 2 years ago
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