Help please, exponential growth and decay question (1 Viewer)

[jscinoz]

Hi,

I've been trying to figure out this question for the past 10 minutes, and I'm just not sure what I'm doing wrong.

The question:
The rate of decrease of barometric pressure, P with respect to height, h, above sea-level is given by the differential equation

If the pressure at sea level is P, show

My attempt:

And from here i'm not sure where to go, since

What am I doing wrong?


Any help would be greatly appreciated,
jscinoz

 

[Fortify]

dP/dh = -kP
dh/dP = -1/kP
h = int (-1/kP) dP
h = (-1/k) int (1/P) dP
h = (-1/k)(ln P) + C1
-kh = lnP + C2
-kh - C2 = lnP
P = e^(-kh - C2)
P = e^(-kh) * e^(C2)
P = Po*e^(-kh)

 

[jscinoz]

I'm with you up to here:

-kh = lnP + C2

where does the second C come from? there's only one integration?

 

[untouchablecuz]

 

[jscinoz]

Ok.. but how do you go from

P = e^(-kh) * e^(C2)

to

P = Po*e^(-kh)

This I'm still unsure of. How do we know e^(C2) is Po?

 

[jscinoz]

Never mind, i figured it out