Thread: 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.

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 ...

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

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.

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

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

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.

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?

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

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!

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