Question

PLEASE HELP!!!

Answer 1

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?

Answer 2

Did you forget something between the words "is" and "thousand"?

Answer 3

I think you're looking for \[\frac{dN}{dt}\]

Answer 4

which can be found by looking at \[\frac{dN}{dt}=\frac{dN}{dp}\frac{dp}{dt}\]

Answer 5

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

Answer 6

so why did dp/dt only come up with the p^2 term and not the 5p term

Answer 7

I'm wondering about that myself actually...

Answer 8

and I'm actually looking for dN/dt according to the way this is making me input my answer

Answer 9

Good gawd - then I really messed that one up... lol

Answer 10

haha its all good I've been messing this one up for about an hour

Answer 11

Let's try that one again... From the top - take two!

Answer 12

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).

Answer 13

right

Answer 14

that was right to the function not to you screwing up by the way haha

Answer 15

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

Answer 16

They're asking for the the rate at which the number of people seeking medical attention is increasing; so dN/dt = ?

Answer 17

That's what we're trying to find. :)

Answer 18

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

Answer 19

well actually thats just going to give us a ridiculously huge number

Answer 20

But, will the number make sense?

Answer 21

What did you get?

Answer 22

no it was like 48 million

Answer 23

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

Answer 24

ya thats what i did

Answer 25

Oh man... I got nothing...

And nothing was left out of the question?

Answer 26

ya i don't get it either man thanks anyway

Answer 27

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.

Answer 28

Wait a sec...

Answer 29

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?"

Answer 30

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." ?

Answer 31

Because if you did, then we should be plugging in 20 instead of 20,000. Actually, that may fix the problem. :)

Answer 32

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.

Answer 33

@TheFigure you already reached the answer: 48,006,000 people seek for emergency care per year!

Answer 34

But he would be entering the answer in wrong if he had those extra zeros attached to the back of it.

Answer 35

You've been right since 30 min before :)