# Thread: Rate of Change Word Problem

1. ## Rate of Change Word Problem

The rate of change of P with respect to h is proportional to p.

p=3 when h=0

p=2 when h=10

p=? when h=50

So far I know to take the derivative of P but I am terrible at word problems and don't know how to set up the equation. Any pointers would help. For example, I get confused when I see things like "with respect to". Any help at all would be appreaciated.

2. ## Re: Rate of Change Word Problem

Originally Posted by Pewter12
The rate of change of P with respect to h is proportional to p.

assuming you meant the same "P" ...

dP/dh = kP

p=3 when h=0

p=2 when h=10

p=? when h=50

So far I know to take the derivative of P but I am terrible at word problems and don't know how to set up the equation. Any pointers would help. For example, I get confused when I see things like "with respect to". Any help at all would be appreaciated.
you are expected to know this basic differential equation has solution ...

$P = P_0 e^{kh}$

3. ## Re: Rate of Change Word Problem

Not sure if this matters but in my manual the first P is capitalized while the second is just lower case p.

4. ## Re: Rate of Change Word Problem

Originally Posted by Pewter12
Not sure if this matters but in my manual the first P is capitalized while the second is just lower case p.
in a strict sense, they would not be the same variable, but, in order to solve the problem with the given information, they would have to be. I would assume the "manual" has a minor typo and both P's are one and the same variable.

5. ## Re: Rate of Change Word Problem

Okay. I guess that makes sense. I still don't understand where the "k" variable comes from, however.

6. ## Re: Rate of Change Word Problem

Originally Posted by Pewter12
Okay. I guess that makes sense. I still don't understand where the "k" variable comes from, however.
k is the constant of proportionality

7. ## Re: Rate of Change Word Problem

Nothing in my manual or text book even briefly alludes to any of this. . . is there any way of actually mathematically figuring the dp/dh=kp as the P=p0ekh at this level? I can't find any relevant examples and the solutions are not given in the text.

8. ## Re: Rate of Change Word Problem

Originally Posted by Pewter12
Nothing in my manual or text book even briefly alludes to any of this. . . is there any way of actually mathematically figuring the dp/dh=kp as the P=p0ekh at this level? I can't find any relevant examples and the solutions are not given in the text.
what do you know about separable differential equations?

9. ## Re: Rate of Change Word Problem

I know that I am not sure what exactly separable differential equations are . . . I suppose I'm in way over my head.

10. ## Re: Rate of Change Word Problem

Originally Posted by Pewter12
I know that I am not sure what exactly separable differential equations are . . . I suppose I'm in way over my head.
sound like you do not have the requisite knowledge to solve this problem.

here is a link to an explanation ...

Calculus Exponential Growth and Decay Word Problems

Thank-you!

12. ## Re: Rate of Change Word Problem

Now that I have read the link and other relevant info from the site I fully understand the question!! Thank-you!!