Math Is Fun Forum

taylor_2009

Member

Registered: 2010-01-25

Posts: 28

Did I do this problem right?

Ecologists estimate that when the population of a certain city is p thousand persons, the average level L of carbon monoxide in the air above the city will be L ppm (parts per million), where L=10+0.4p+0.0001p². The population of the city is estimated to be p=752+23t+0.5t² thousand persons t years from the present.

a)Find the rate of change of carbon monoxide with respect to time.

I got: L=10+4(752+23t+0.5t²)+0.0001(752+23t+0.5t²)²

dL/dt = 4(23+t)+0.0002((752+23t+0.5t²)(23+t)
        =(23+t)(4.1504+0.0046t+0.0001t²)

b)Find the time rate of change of the population (the rate of change of the population with respect to time)

I got: dp/dt = 23+t

c)How fast (with respect to time) is the carbon monoxide level changing at time t=2?

You would use the dL/dt right and substitute 2 in for t? I got the answer of 104 ppm/yr but I think that sounds high so I'm not sure.

Any help is appreciated!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Did I do this problem right?

Hi taylor_2009

b is correct.

Check your dL / dt you have made an arithmetic mistake.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

taylor_2009

Member

Registered: 2010-01-25

Posts: 28

Re: Did I do this problem right?

Did I do the derivative right or was it in the simplifying? Thanks.

Last edited by taylor_2009 (2010-03-17 17:16:27)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Did I do this problem right?

On the substitution where you put p into L

p=752+23t+0.5t²

L=10+0.4p+0.0001p²

There is a cataclysmic error

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

taylor_2009

Member

Registered: 2010-01-25

Posts: 28

Re: Did I do this problem right?

I did it again and got the exact same answer.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Did I do this problem right?

Hi taylor_2009;

I got: L=10+4(752+23t+0.5t²)+0.0001(752+23t+0.5t²)²

You changed a .4 to a 4

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

taylor_2009

Member

Registered: 2010-01-25

Posts: 28

Re: Did I do this problem right?

Oh oops. Shouldn't do math late at night haha

For dL/dt I got (23+t)(0.5504+.0046t+0.0001t²) and for part c I got 14 ppm/yr.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Did I do this problem right?

Now, that's correct. I got 14 ppm also.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.